Question

34. If A is any skew-symmetric $\mathbf{4}\mathbf{\times }\mathbf{4}$matrix, then detA = 0.

Short answer

Therefore,$detA\ne 0$the given statement is not satisfied.

Step-by-step solution

Matrix Definition

Matrix is a set of numbers arranged in rows andcolumns so as to form a rectangular array.

The numbers are called the elements, or entries, of the matrix.

If there are m rows and n columns, the matrix is said to be an “m by n” matrix, written “$m\times n$.”

To check whether the given condition is true or false

For example $4\times 4$matrix,

$A=\left[\begin{array}{cccc}1& 1& 0& 0\\ -1& 1& 0& 0\\ 0& 0& 1& 0\\ 0& 0& 0& 1\end{array}\right]$

is a skew-symmetric $4\times 4$matrix, yet det A = 2

Therefore,

$detA\ne 0$.

Thus,$detA\ne 0$ the given statement is not satisfied.