MATRICES, Commerce Maths 1, Exercise 2.1 | Q 1.1 | Page 39

Exercise 2.1 | Q 1.1 | Page 39

Construct  a matrix A = ${\displaystyle {\left[a_{\text{ij}}\right]}_{3\times 2}}$ whose element a_ij is given by

a_ij = ${\displaystyle \frac{{(i-j)}^2}{5-i}}$

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Exercise 2.1 | Q 1.2 | Page 39

Construct a matrix A = ${\displaystyle {\left[a_{\text{ij}}\right]}_{3\times 2}}$ whose element a_ij is given by

a_ij = i – 3j

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Exercise 2.1 | Q 1.3 | Page 39

Construct a matrix A = ${\displaystyle {\left[a_{\text{ij}}\right]}_{3\times 2}}$ whose element a_ij is given by

a_ij = ${\displaystyle \frac{{(i+j)}^3}{5}}$

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Exercise 2.1 | Q 2.1 | Page 39

Classify each of the following matrices as a row, a column, a square, a diagonal, a scalar, a unit, an upper traingular, a lower triangular matrix.

${\displaystyle \left[\begin{array}{ccc}3& -2& 4\\ 0& 0& -5\\ 0& 0& 0\end{array}\right]}$

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Exercise 2.1 | Q 2.2 | Page 39

Classify each of the following matrices as a row, a column, a square, a diagonal, a scalar, a unit, an upper traingular, a lower triangular matrix.

${\displaystyle \left[\begin{array}{c}5\\ 4\\ -3\end{array}\right]}$

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Exercise 2.1 | Q 2.3 | Page 39

Classify each of the following matrices as a row, a column, a square, a diagonal, a scalar, a unit, an upper triangular, a lower triangular matrix.

${\displaystyle [9 \sqrt{2} -3]}$

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Exercise 2.1 | Q 2.4 | Page 39

Classify each of the following matrices as a row, a column, a square, a diagonal, a scalar, a unit, an upper traingular, a lower triangular matrix.

${\displaystyle \left[\begin{array}{cc}6& 0\\ 0& 6\end{array}\right]}$

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Exercise 2.1 | Q 2.5 | Page 39

Classify each of the following matrices as a row, a column, a square, a diagonal, a scalar, a unit, an upper traingular, a lower triangular matrix.

${\displaystyle \left[\begin{array}{ccc}2& 0& 0\\ 3& -1& 0\\ -7& 3& 1\end{array}\right]}$

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Exercise 2.1 | Q 2.6 | Page 39

Classify each of the following matrices as a row, a column, a square, a diagonal, a scalar, a unit, an upper traingular, a lower triangular matrix.

${\displaystyle \left[\begin{array}{ccc}3& 0& 0\\ 0& 5& 0\\ 0& 0& \frac{1}{3}\end{array}\right]}$

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Exercise 2.1 | Q 2.7 | Page 39

Classify each of the following matrices as a row, a column, a square, a diagonal, a scalar, a unit, an upper triangular, a lower triangular matrix.

${\displaystyle \left[\begin{array}{ccc}1& 0& 0\\ 0& 1& 0\\ 0& 0& 1\end{array}\right]}$

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Exercise 2.1 | Q 3.1 | Page 39

Which of the following matrices are singular or non singular?

${\displaystyle \left[\begin{array}{ccc}\text{a}& \text{b}& \text{c}\\ \text{p}& \text{q}& \text{r}\\ 2\text{a}-\text{p}& 2\text{b}-\text{q}& 2\text{c}-\text{r}\end{array}\right]}$

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Exercise 2.1 | Q 3.2 | Page 39

Which of the following matrices are singular or non singular?

${\displaystyle \left[\begin{array}{ccc}5& 0& 5\\ 1& 99& 100\\ 6& 99& 105\end{array}\right]}$

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Exercise 2.1 | Q 3.3 | Page 40

Which of the following matrices are singular or non singular?

${\displaystyle \left[\begin{array}{ccc}3& 5& 7\\ -2& 1& 4\\ 3& 2& 5\end{array}\right]}$

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Exercise 2.1 | Q 3.4 | Page 40

Which of the following matrices are singular or non singular?

${\displaystyle \left[\begin{array}{cc}7& 5\\ -4& 7\end{array}\right]}$

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Exercise 2.1 | Q 4.1 | Page 40

Find K if the following matrices are singular.

${\displaystyle \left[\begin{array}{cc}7& 3\\ -2& \text{K}\end{array}\right]}$

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Exercise 2.1 | Q 4.2 | Page 40

Find K if the following matrices are singular.

${\displaystyle \left[\begin{array}{ccc}4& 3& 1\\ 7& \text{K}& 1\\ 10& 9& 1\end{array}\right]}$

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Exercise 2.1 | Q 4.3 | Page 40

Find K if the following matrices are singular.

${\displaystyle \left[\begin{array}{ccc}\text{K}-1& 2& 3\\ 3& 1& 2\\ 1& -2& 4\end{array}\right]}$

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