Construct a matrix A = \( [a_{ij}]_{3 \times 2} \) whose element \( a_{ij} \) is given by
\( a_{ij} = \frac{(i-j)^2}{5-i} \)
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Exercise 2.1 | Q 1.2 | Page 39
Construct a matrix A = \( [a_{ij}]_{3 \times 2} \) 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 = \( [a_{ij}]_{3 \times 2} \) whose element \( a_{ij} \) is given by
\( a_{ij} = \frac{(i+j)^3}{5} \)
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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 triangular, a lower triangular matrix.
\[ \begin{bmatrix} 3 & -2 & 4 \\ 0 & 0 & -5 \\ 0 & 0 & 0 \end{bmatrix} \]
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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 triangular, a lower triangular matrix.
\[ \begin{bmatrix} 5 \\ 4 \\ -3 \end{bmatrix} \]
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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.
\[ \begin{bmatrix} 9 & \sqrt{2} & -3 \end{bmatrix} \]
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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 triangular, a lower triangular matrix.
\[ \begin{bmatrix} 6 & 0 \\ 0 & 6 \end{bmatrix} \]
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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 triangular, a lower triangular matrix.
\[ \begin{bmatrix} 2 & 0 & 0 \\ 3 & -1 & 0 \\ -7 & 3 & 1 \end{bmatrix} \]
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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 triangular, a lower triangular matrix.
\[ \begin{bmatrix} 3 & 0 & 0 \\ 0 & 5 & 0 \\ 0 & 0 & \frac{1}{3} \end{bmatrix} \]
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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.
\[ \begin{bmatrix} 1 & 0 & 0 \\ 0 & 1 & 0 \\ 0 & 0 & 1 \end{bmatrix} \]
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Exercise 2.1 | Q 3.1 | Page 39
Which of the following matrices are singular or non singular?
\[ \begin{bmatrix} a & b & c \\ p & q & r \\ 2a-p & 2b-q & 2c-r \end{bmatrix} \]
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Exercise 2.1 | Q 3.2 | Page 39
Which of the following matrices are singular or non singular?
\[ \begin{bmatrix} 5 & 0 & 5 \\ 1 & 99 & 100 \\ 6 & 99 & 105 \end{bmatrix} \]
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Exercise 2.1 | Q 3.3 | Page 40
Which of the following matrices are singular or non singular?
\[ \begin{bmatrix} 3 & 5 & 7 \\ -2 & 1 & 4 \\ 3 & 2 & 5 \end{bmatrix} \]
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Exercise 2.1 | Q 3.4 | Page 40
Which of the following matrices are singular or non singular?
\[ \begin{bmatrix} 7 & 5 \\ -4 & 7 \end{bmatrix} \]
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Exercise 2.1 | Q 4.1 | Page 40
Find K if the following matrices are singular.
\[ \begin{bmatrix} 7 & 3 \\ -2 & K \end{bmatrix} \]
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Exercise 2.1 | Q 4.2 | Page 40
Find K if the following matrices are singular.
\[ \begin{bmatrix} 4 & 3 & 1 \\ 7 & K & 1 \\ 10 & 9 & 1 \end{bmatrix} \]
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Exercise 2.1 | Q 4.3 | Page 40
Find K if the following matrices are singular.
\[ \begin{bmatrix} K-1 & 2 & 3 \\ 3 & 1 & 2 \\ 1 & -2 & 4 \end{bmatrix} \]
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