Matrices Class 12th Mathematics Part I CBSE Solution

Class 12^th Mathematics Part I CBSE Solution

Exercise 3.1

1. In a matrix A = a^n = [cccc 2&5&19&-7 35&-2& 5/2 &12 root 3 &1&-5&17] , (i) The…
2. If a matrix has 24 elements, what are the possible orders it can have? What, if…
3. If a matrix has 18 elements, what are the possible orders it can have? What, if…
4. a_ij = (i+j)^2/2 Construct a 2 × 2 matrix, A = [aij], whose elements are given…
5. a_ij = i/j Construct a 2 × 2 matrix, A = [aij], whose elements are given by:…
6. a_ij = (i+2j)^2/2 Construct a 2 × 2 matrix, A = [aij], whose elements are given…
7. a_ij = 1/2 |-3i+j| Construct a 3 × 4 matrix, whose elements are given by:…
8. a_ij = 2i-j Construct a 3 × 4 matrix, whose elements are given by:…
9. [ll 4&3 x&5] = [ll y 1&5] Find the values of x, y and z from the following…
10. [cc x+y&2 5+z] = [ll 6&2 5&8] Find the values of x, y and z from the following…
11. [c x+y+z x+z y+z] = [9 5 7] Find the values of x, y and z from the following…
12. Find the value of a, b, c and d from the equation: [cc a-b&2a+c 2a-b&3c+d] = [cc…
13. A = [aij]m × n is a square matrix, ifA. m n B. m n C. m = n D. None of these…
14. Which of the given values of x and y make the following pair of matrices equal…
15. The number of all possible matrices of order 3 × 3 with each entry 0 or 1 is:A.…

Exercise 3.2

1. Le t a = [ll 2&4 3&2] , b = [cc 1&3 -2&5] , c = [cc -2&5 3&4] Find each of the…
2. Let a = [ll 2&4 3&2] , b = [rr 1&3 -2&5] , c = [cc -2&5 3&4] Find each of the…
3. Let a = [ll 2&4 3&2] , b = [rr 1&3 -2&5] , c = [cc -2&5 3&4] Find each of the…
4. Let a = [ll 2&4 3&2] , b = [rr 1&3 -2&5] , c = [cc -2&5 3&4] Find each of the…
5. Let a = [ll 2&4 3&2] , b = [rr 1&3 -2&5] , c = [cc -2&5 3&4] Find each of the…
6. [cc a -b] + [ll a b] Compute the following:
7. [cc a^2 + b^2 & b^2 + c^2 a^2 + c^2 & a^2 + b^2] + [cc 2ab&2bc -2ac&-2ab]…
8. [ccc -1&4&-6 8&5&16 2&8&5] + [ccc 12&7&6 8&0&5 3&2&4] Compute the following:…
9. [cc cos^2x^2x sin^2x^2x] + [cc sin^2x^2x cos^2x^2x] Compute the following:…
10. Compute the indicated products.
11. [1 2 3] [lll 2&3&4] Compute the indicated products.
12. [cc 1&-2 2&3] [ccc 1&2&3 2&3&1] Compute the indicated products.
13. [ccc 2&3&4 3&4&5 4&5&6] [ccc 1&-3&5 0&2&4 3&0&5] Compute the indicated…
14. Compute the indicated products.
15. [ccc 3&-1&3 -1&0&2] [cc 2&-3 1&0 3&1] Compute the indicated products.…
16. If a = [ccc 1&2&-3 5&0&2 1&-1&1] , b = [ccc 3&-1&2 4&2&5 2&0&3] c = [ccc 4&1&2…
17. If a = [ccc 2/3 &1& 5/3 1/3 & 2/3 & 4/3 7/3 &2& 2/3] b = [ccc 2/5 & 3/5 &1 1/5 &…
18. Simplify costheta [cc costheta heta -sintegrate heta]+sintegrate heta [cc…
19. x+y = [ll 7&0 2&5] x-y = [ll 3&0 0&3] Find X and Y, if
20. 2x+3y = [ll 2&3 4&0] 3x+2y = [cc 2&-2 -1&5] Find X and Y, if
21. Find X, if y = [ll 3&2 1&4] 2x+y = [cc 1&0 -3&2]
22. Find x and y, if 2 [ll 1&3 0] + [ll y&0 1&2] = [ll 5&6 1&8]
23. Solve the equation for x, y, z and t, if 2 [ll x y]+3 [cc 1&-1 0&2] = 3 [cc 3&5…
24. If x [2 3]+y [c -1 1] = [c 10 5] , find the values of x and y.
25. Given 3 [cc x z] = [cc x&6 -1&2w] + [cc 4+y z+w&3] , find the values of x, y, z…
26. If f (x) = [ll cosx&-sinx&0 sinx&0 0&0&1 show that F(x) F(y) = F(x + y).…
27. [cc 5&-1 6&7] [cc 2&1 3&4] not equal [ll 2&1 3&4] [cc 5&-1 6&7] Show that…
28. [ccc 1&2&3 0&1&0 1&1&0] [ccc -1&1&0 0&-1&1 2&3&4] = [ccc -1&1&0 0&-1&1 2&3&4]…
29. Find A^2 - 5A + 6I, if a = [lll 2&0&1 2&1&3 1&-1&0]
30. If a = [lll 1&0&2 0&2&1 2&0&3] , prove that A3 - 6A^2 + 7A + 2I = 0…
31. If a = [ll 3&-2 4&-2] i = [ll 1&0 0&1] , find k so that A^2 = kA - 2I…
32. If a = [ccc 0& - tan alpha /2 tan alpha /2 &0] and I is the identity matrix of…
33. Rs 1800 A trust fund has Rs. 30,000 that must be invested in two different…
34. Rs. 2000 A trust fund has Rs. 30,000 that must be invested in two different…
35. The bookshop of a particular school has 10 dozen chemistry books, 8 dozen…
36. The restriction on n, k and p so that PY + WY will be defined are:A. k = 3, p =…
37. If n = p, then the order of the matrix 7X - 5Z is:A. p × 2 B. 2 × n C. n × 3 D.…

Exercise 3.3

1. [c 5 1/2 -1] Find the transpose of each of the following matrices:…
2. [cc 1&-1 2&3] Find the transpose of each of the following matrices:…
3. [ccc -1&5&6 root 3 &5&6 2&3&-1] Find the transpose of each of the following…
4. If a = [ccc -1&2&3 5&7&9 -2&1&1] and, then verify that (A + B)’ = A’ + B’,…
5. If a = [ccc -1&2&3 5&7&9 -2&1&1] and, then verify that (A - B)’ = A’- B’…
6. If a^there there eξ sts = [cc 3&4 -1&2 0&1] and, then verify that (A + B). = A’…
7. If a^there there eξ sts = [cc 3&4 -1&2 0&1] and, then verify that (A - B)’ =…
8. If a = [rr -2&3 1&2] and b = [rr -1&0 1&2] , then find (A + 2B)’
9. (i) a = [c 1 -4 3] b = [lll -1&2&1] For the matrices A and B, verify that (AB)’…
10. b = [lll 1&5&7]a = [0 1 2] For the matrices A and B, verify that (AB)’ = B’A’,…
11. If a = [ll cosalpha -sinalpha] , then verify that A’ A = I
12. If a = [cc sinalpha -cosalpha] , then verify that A’ A = I
13. Show that the matrix a = [ccc 1&-1&5 -1&2&1 5&1&3] is a symmetric matrix.…
14. Show that the matrix a = [ccc 0&1&-1 -1&0&1 1&-1&0] is a skew symmetric matrix.…
15. For the matrix a = [ll 1&5 6&7] , verify that (A + A’) is a symmetric matrix…
16. For the matrix a = [ll 1&5 6&7] , verify that (A - A’) is a skew symmetric…
17. Find and 1/2 (a-a^there there eξ sts) , when a = [ccc 0 -a&0 -b&-c&0]…
18. [cc 3&5 1&-1] Express the following matrices as the sum of a symmetric and a…
19. [ccc 6&-2&2 -2&3&-1 2&-1&3] Express the following matrices as the sum of a…
20. [ccc 3&3&-1 -2&-2&1 -4&-5&2] Express the following matrices as the sum of a…
21. [cc 1&5 -1&2] [cc 3&5 1&-1] Express the following matrices as the sum of a…
22. If A, B are symmetric matrices of same order, then AB - BA is aA. Skew…
23. If , and A + A’ = I, if the value of a isA. 3 pi /2 B. pi /3 C. pi D. 3 pi /2…

Exercise 3.4

1. Using elementary transformations, find the inverse of each of the matrices.…
2. [ll 2&1 1&1] Using elementary transformations, find the inverse of each of the…
3. [ll 1&3 2&7] Using elementary transformations, find the inverse of each of the…
4. [ll 2&3 5&7] Using elementary transformations, find the inverse of each of the…
5. [ll 2&1 7&4] Using elementary transformations, find the inverse of each of the…
6. [ll 2&5 1&3] Using elementary transformations, find the inverse of each of the…
7. [ll 3&1 5&2] Using elementary transformations, find the inverse of each of the…
8. [ll 4&5 3&4] Using elementary transformations, find the inverse of each of the…
9. [cc 3&10 2&7] Using elementary transformations, find the inverse of each of the…
10. [cc 3&-1 -4&2] Using elementary transformations, find the inverse of each of…
11. [ll 2&-6 1&-2] Using elementary transformations, find the inverse of each of…
12. [cc 6&-3 -2&1] Using elementary transformations, find the inverse of each of…
13. [cc 2&-1 -3&2] Using elementary transformations, find the inverse of each of…
14. [ll 2&1 4&2] Using elementary transformations, find the inverse of each of the…
15. [ccc 2&-3&3 2&2&3 3&-2&2] Using elementary transformations, find the inverse of…
16. [ccc 1&3&-2 -3&0&-5 2&5&0] Using elementary transformations, find the inverse…
17. [ccc 2&0&-1 5&1&0 0&1&3] Using elementary transformations, find the inverse of…
18. Matrices A and B will be inverse of each other only ifA. AB = BA B. AB = BA = 0…

Miscellaneous Exercise

1. Let, show that (aI + bA)n = anI + nan-1bA, where I is the identity matrix of…
2. If a = [lll 1&1&1 1&1&1 1&1&1] , prove that .
3. If a = [ll 3&-4 1&-1] then prove that a^n = [cc 1+2n&-4n n&1-2n] where n is any…
4. If A and B are symmetric matrices, prove that AB - BA is a skew symmetric…
5. Show that the matrix B’AB is symmetric or skew symmetric according as A is…
6. Find the values of x, y, z if the matrix satisfy a = [ccc 0&2y x&-z x&-y] the…
7. For what values of x: [lll 1&2&1] [lll 1&2&0 2&0&1 1&0&2] [0 2 x] = 0?…
8. If a = [cc 3&1 -1&2] show that A^2 - 5A + 7I =0.
9. Find x, if [rrr x&-5&-1] [lll 1&0&2 0&2&1 2&0&3] [x 4 1] = 0
10. A manufacturer produces three products x, y, z which he sells in two markets.…
11. Find the matrix X so that x [ccc 1&2&3 4&5&6] = [ccc -7&-8&-9 2&4&6]…
12. If A and B are square matrices of the same order such that AB = BA, then prove…
13. If a = [ll alpha & beta gamma & - alpha] is such that A � = I, thenA. 1 +…
14. If the matrix A is both symmetric and skew symmetric, thenA. A is a diagonal…
15. If A is square matrix such that A^2 = A, then (I + A)^3 7 A is equal toA. A B.…

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Exercise 3.1

Question 1.

In a matrix A =



(i) The order of the matrix,

(ii) The number of elements,

(iii) Write the elements a₁₃, a₂₁, a₃₃, a₂₄, a₂₃.

Answer:

(i) In the given matrix, the number of rows is 3 and the number of columns is 4.

Order of a matrix =No of rows × No of columns

Therefore, the order of the matrix is 3 × 4.

(ii) Since, the order of the matrix is 3 × 4, there are 3 × 4 = 12 elements in it.

(iii) a₁₃ = 19, a₂₁ = 35, a₃₃ = -5, a₂₄ = 12, a₂₃ = .

Question 2.

If a matrix has 24 elements, what are the possible orders it can have? What, if it has 13 elements?

Answer:

It is known that if a matrix is of the order m × n, then it has mn elements.

Therefore, to find all the possible orders of a matrix having 24 elements, we had to find all the ordered pairs of natural numbers whose product is 24.

The ordered pairs are: (1, 24), (24, 1), (2, 12), (12, 2), (3, 8), (8, 3), (4, 6), and (6, 4).

Therefore, the possible orders of a matrix having 24 elements are;

1 × 24, 24 × 1, 2 × 12, 12 × 2, 3 × 8, 8 × 3, 4 × 6, 6 × 4

(1, 13) and (13, 1) are the ordered pairs of natural numbers whose product is 13.

Therefore, the possible orders of a matrix having 13 elements are 1 × 13 and 13 × 1.

Question 3.

If a matrix has 18 elements, what are the possible orders it can have? What, if it has 5 elements?

Answer:

It is known that if a matrix s of the order m × n, then it has mn elements.

Therefore, to find all the possible orders of a matrix having 18 elements, we had to find all the ordered pairs of natural numbers whose product is 18.

The ordered pairs are: (1, 18), (18, 1), (2, 9), (9, 2), (3, 6) and (6, 3).

Therefore, the possible orders of a matrix having 24 elements are;

1 × 18, 18 × 1, 2 × 9, 9 × 2, 3 × 6, 6 × 3

(1, 5) and (5, 1) are the ordered pairs of natural numbers whose product is 5.

Therefore, the possible orders of a matrix having 5 elements are 1 × 5 and 5 × 1.

Question 4.

Construct a 2 × 2 matrix, A = [a_ij], whose elements are given by:

Answer:

In general, a 2 × 2 matrix is given by A = 

a_ij = 

Therefore,

a₁₁ = 

a₁₂ = 

a₂₁ = 

a₂₂ = 

Therefore, the required matrix is A = 

Question 5.

Construct a 2 × 2 matrix, A = [a_ij], whose elements are given by:

Answer:

In general, a 2 × 2 matrix is given by A = 

a_ij = 

Therefore,

a₁₁ = 

a₁₂ = 

a₂₁ = 

a₂₂ = 

Therefore, the required matrix is A = .

Question 6.

Construct a 2 × 2 matrix, A = [a_ij], whose elements are given by:

Answer:

In general, a 2 × 2 matrix is given by A = 

a_ij = 

Therefore,

a₁₁ = 

a₁₂ = 

a₂₁ = 

a₂₂ = 

Therefore, the required matrix is A = 

Question 7.

Construct a 3 × 4 matrix, whose elements are given by:

Answer:

In general 3 × 4 matrix is given by A = 

Therefore,

a₃₂ = 

a₁₃ = 

a₂₃ = 

a₃₃ = 

a₁₄ = 

a₂₄ = 

a₃₄ = 

Therefore, required matrix is A = 

Question 8.

Construct a 3 × 4 matrix, whose elements are given by:

Answer:

In general 3 × 4 matrix is given by A = 

a_ij = 2i-j, i = 1,2,3 and j = 1,2,3,4

Therefore,

a₁₁ = 2 × 1 - 1 = 2 - 1 = 1

a₂₁ = 2 × 2 - 1 = 4 - 1 = 3

a₃₁ = 2 × 3 - 1 = 6 - 1 = 5

a₁₂ = 2 × 1 - 2 = 2 - 2 = 0

a₂₂ = 2 × 2 - 2 = 4 - 2 = 2

a₃₂ = 2 × 3 - 2 = 6 - 2 = 4

a₁₃ = 2 × 1 - 3 = 2 - 3 = -1

a₂₃ = 2 × 2 - 3 = 4 - 3 = 1

a₃₃ = 2 × 3 - 3 = 6 - 3 = 3

a₁₄ = 2 × 1 - 4 = 2 - 4 = -2

a₂₄ = 2 × 2 - 4 = 4 - 4 = 0

a₃₄ = 2 × 3 - 4 = 6 - 4 = 2

Therefore, required matrix is A = 

Question 9.

Find the values of x, y and z from the following equations:

Answer:

Since, the given matrices are equal, their corresponding elements are also equal.

Comparing the corresponding element, we have:

x = 1, y = 4 and z = 3

Question 10.

Find the values of x, y and z from the following equations:

Answer:

Since, the given matrices are equal, their corresponding elements are also equal.

Comparing the corresponding element, we have:

x + y = 6, xy = 8, 5 + z = 5

Now, 5 + z = 5
⇒ z = 0

x+ y = 6
⇒ x = 6 - y 

Also, 
xy = 8
⇒ (6 - y)y = 8
⇒ 6y - y²= 8
⇒ y² - 6y + 8 = 0
⇒ y² - 4y - 2y + 8 = 0
⇒ y(y - 4) - 2(y - 4) = 0
⇒ (y - 2)(y - 4) = 0

Hence, y = 2 or y = 4
when y = 2 
x = 6 - 2 = 4

when x = 4
x = 6 - 4 = 2


Question 11.

Find the values of x, y and z from the following equations:

Answer:

Since, the given matrices are equal, their corresponding elements are also equal.

Comparing the corresponding element, we have:

x + y + z = 9...(1)

x + z = 5.....(2)

y + z = 7.......(3)

Putting the value of equation 2 in equation 1,

y + 5 = 9

⇒ y = 4

Then, putting the value of y in equation 3, we get,

4 + z = 7

⇒ z = 3

Therefore, x + z = 5

⇒ x = 2

Therefore, x =2, y = 4 and z = 3.

Question 12.

Find the value of a, b, c and d from the equation:

Answer:

Since, the given matrices are equal, their corresponding elements are also equal.

Comparing the corresponding element, we have:

a –b = -1 …(1)

2a – b = 0 …(2)

2a + c = 5 …(3)

3c + d = 13 …(4)

From equation (2), we get:

b = 2a

Then, from eq. (1), we get,

a -2a = -1

⇒ a = 1

⇒ b = 2

Now, from eq. (3), we get:

2 × 1 + c = 5

⇒ c = 3

From (4), we get,

3 × 3 + d = 13

⇒ 9 + d = 13

⇒ d = 4

Therefore, a = 1, b = 2, c = 3 and d = 4.

Question 13.

A = [a_ij]_{m × n} is a square matrix, if
A. m < n

B. m > n

C. m = n

D. None of these

Answer:

We know that if a given matrix is said to be square matrix if the number of rows is equal to the number of columns.

Therefore, A = [a_ij]_{m × n} is a square matrix, if m = n.

Question 14.

Which of the given values of x and y make the following pair of matrices equal


A. 

B. Not possible to find

C. y = 7, 

D. 

Answer:

Now, 

Since, the given matrices are equal, their corresponding elements are also equal.

Comparing the corresponding element, we have:

3x + 7 = 0

5 = y – 2

⇒ y = 7

y + 1 = 8

⇒ y = 7

And 2 – 3x = 4

Thus, on comparing the corresponding elements of the two matrices, we get different values of x, which is not possible.

Therefore, it is not possible to find the values of x and y for which the given matrices are equal.

Question 15.

The number of all possible matrices of order 3 × 3 with each entry 0 or 1 is:
A. 27

B. 18

C. 81

D. 512

Answer:

The given matrix of the order 3 × 3 has 9 elements with each entry 0 or 1.

Now, each of the 9 elements can be filled in two possible ways.

Hence, the required number of possible matrices is 2⁹ = 512.

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Exercise 3.2

Question 1.

Le t 
Find each of the following:

i) A + B
ii) A - B
iii) 3A - C
iv) AB
v) BA

Answer:

i) A + B = 

ii) A - B








iii) 3A - C







iv) AB





v) BA

Question 2.

Let 

Find each of the following:

A – B

Answer:

A – B = 

Question 3.

Let 

Find each of the following:

3A – C

Answer:

3A – C = 

Question 4.

Let 

Find each of the following:

AB

Answer:

AB 

Question 5.

Let 

Find each of the following:

BA

Answer:

BA = 

Question 6.

Compute the following:

Answer:

Question 7.

Compute the following:

Answer:

.

Question 8.

Compute the following:

Answer:

Question 9.

Compute the following:

Answer:

Question 10.

Compute the indicated products.

Answer:

Question 11.

Compute the indicated products.

Answer:

Question 12.

Compute the indicated products.

Answer:

Question 13.

Compute the indicated products.

Answer:

.

.

Question 14.

Compute the indicated products.

Answer:

Question 15.

Compute the indicated products.

Answer:

Question 16.

If  then compute (A + B) and (B – C). Also, verify that A + (B – C) = (A + B) – C.

Answer:

Now, A+ B 

B – C 

A + (B –C) 

.

+ B) – C = 

.

Therefore, A + (B –C) = (A + B) – C

Question 17.

If  then compute 3A – 5B.

Answer:

3A – 5B 

Question 18.

Simplify 

Answer:

.

Question 19.

Find X and Y, if

Answer:

Now, X + Y =  …(1)

Adding (1) and (2), we get,

2X = 

.

Now, X + Y = 

Question 20.

Find X and Y, if

Answer:

2X + 3Y  …(1)

3X + 2Y  …(2)

Now, multiply equation (1) by 2 and equation (2) by 3, we get,

4X + 6Y  …(3)

9X + 6Y  …(4)

Subtracting equation (4) from (3), we get,

(4X + 6Y) – (9X + 6Y)

Now, 2X + 3Y 

Question 21.

Find X, if 

Answer:

2X + Y 

Question 22.

Find x and y, if 

Answer:

Now, on comparing elements of these two matrices, we get,

2 + y = 5

=> y = 3

And 2x + 2 = 8

=> x = 3

Therefore, x = 3 and y = 3.

Question 23.

Solve the equation for x, y, z and t, if 

Answer:

On comparing the elements of these two matrices, we get,

2x + 3 = 9

⇒ 2x = 6

⇒ x = 3

2y = 12

⇒ y = 6

2z -3 = 15

⇒ 2z = 18

⇒ z = 9

2t +6 = 18

⇒ 2t = 12

⇒ t = 6

Therefore, x = 3, y =6, z = 9 and t = 6.

Question 24.

If , find the values of x and y.

Answer:

On comparing the corresponding elements of these two matrices, we get,

2x –y = 10 and 3x + y =5

Now, adding above two equations, we get

5x = 15

⇒ x = 3

Now, 3x + y = 5

⇒ y = 5 - 3x

⇒ y = 5 - 9 = -4

Therefore, x = 3 and y = -4.

Question 25.

Given , find the values of x, y, z and w.

Answer:

On comparing the corresponding elements of these two matrices, we get,

3x = x + 4

⇒ 2x + 4

⇒ x =2

3y = 6 + x + y

⇒ 2y = 6 + x = 6 + 2 = 8

⇒ y = 4

3w = 2w + 3

⇒ w = 3

3z = -1 + z + w

⇒ 2z = -1 + w = -1 +3 = 2

⇒ z = 1

Therefore, x = 2, y = 4, z = 1 and w = 3.

Question 26.

If  show that F(x) F(y) = F(x + y).

Answer:

Therefore, F(x)F(y) = F(x+y)

Question 27.

Show that

Answer:

Question 28.

Show that

Answer:

Question 29.

Find A² – 5A + 6I, if 

Answer:

A² = A.A 

Now, A² – 5A + 6I 

Question 30.

If, prove that A₃ – 6A² + 7A + 2I = 0

Answer:

A² = A.A 

Now, A³ = A². A

Now, A³ – 6A² + 7A + 2I 

Therefore, A³ – 6A² + 7A + 2I = 0

Question 31.

If , find k so that A² = kA – 2I

Answer:

A² = A.A 

Now, A² = kA – 2I

Comparing the corresponding elements, we get,

3k -2 = 1

⇒ 3k = 3

⇒ k = 1

Therefore, the value of k is 1.

Question 32.

If  and I is the identity matrix of order 2, show that 

Answer:

We know that I 

Now, LHS = I + A 

=

And on RHS = (I – A)

As we know,

cos 2θ = 1 - 2 sin² θ

cos 2θ = 2 cos² θ - 1

and sin2θ = 2 sinθ cosθ

As tanθ = sinθ/cosθ

=

= LHS

Hence Proved.

Question 33.

A trust fund has Rs. 30,000 that must be invested in two different types of bonds. The first bond pays 5% interest per year, and the second bond pays 7% interest per year. Using matrix multiplication, determine how to divide Rs. 30,000 among the two types of bonds. If the trust fund must obtain an annual total interest of:

Rs 1800

Answer:

(a) Let Rs x be invested in the first bond.

Then, the sum of money invested in the second bond will be Rs. (30000 – x).

It is given that the first bond pays 5% interest per year, and the second bond pays 7% interest per year.

Thus, in order to obtain an annual total interest of Rs. 1800, we get:

⇒ 5x + 210000 -7x = 180000

⇒ 210000 -2x = 180000

⇒ 2x = 210000 – 180000

⇒ 2x = 30000

⇒ x = 15000

Therefore, in order to obtain an annual total interest of Rs. 1800, the trust fund should invest Rs. 15000 in the first bond and the remaining Rs. 15000 in the second bond.

Question 34.

A trust fund has Rs. 30,000 that must be invested in two different types of bonds. The first bond pays 5% interest per year, and the second bond pays 7% interest per year. Using matrix multiplication, determine how to divide Rs. 30,000 among the two types of bonds. If the trust fund must obtain an annual total interest of:

Rs. 2000

Answer:

(a) Let Rs x be invested in the first bond.

Then, the sum of money invested in the second bond will be Rs (30000 – x).

It is given that the first bond pays 5% interest per year, and the second bond pays 7% interest per year.

Thus, in order to obtain an annual total interest of Rs 1800, we get: