Maharashtra Board Solutions for Chapter: Determinants and Matrices, Exercise 5: EXERCISE 4.4

Construct a matrix $A=[a_{ij}{]}_{3\times 2}$ whose elements $a_{ij}$  are given by $a_{ij}=\frac{(i-j{)}^2}{5-i}$.

Construct a matrix $A=[a_{ij}{]}_{3\times 2}$ whose elements $a_{ij}$ are given by $a_{ij}=i–3j$.

Construct a matrix $A=[a_{ij}{]}_{3\times 2}$ whose elements $a_{ij}$  are given by $a_{ij}=\frac{(i+j{)}^3}{5}$.

Classify the following matrices as, a row, a column, a square, a diagonal, a scalar, a unit, an upper triangular, a lower triangular, a symmetric or a skew-symmetric matrix.

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

Classify the following matrices as, a row, a column, a square, a diagonal, a scalar, a unit, an upper triangular, a lower triangular, a symmetric or a skew-symmetric matrix.

$\left[\begin{array}{ccc}0& 4& 7\\ -4& 0& -3\\ -7& 3& 0\end{array}\right]$

Classify the following matrices as, a row, a column, a square, a diagonal, a scalar, a unit, an upper triangular, a lower triangular, a symmetric or a skew-symmetric matrix.

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

Classify the following matrix as, a row, a column, a square, a diagonal, a scalar, a unit, an upper triangular, a lower triangular, a symmetric or a skew-symmetric matrix: $\left[\begin{array}{ccc}1& 0& 0\\ 0& 1& 0\\ 0& 0& 1\end{array}\right]$

Classify the following matrix as, a row, a column, a square, a diagonal, a scalar, a unit, an upper triangular, a lower triangular, a symmetric or a skew-symmetric matrix: $\left[\begin{array}{ccc}0& 0& 1\\ 0& 1& 0\\ 1& 0& 0\end{array}\right]$