Question

What should be the value of x so that the matrix (2/8 4/x) does not have an inverse?

Answer 1

Step-by-step explanation:

Given:

$A=\left[\begin{array}{cc}2&4\\8&x\end{array}\right]$

To find:What should be the value of x so that the matrix A does not have an inverse?

Solution: We know that if matrix A is Singular matrix

i.e. Determinant of A is zero, then A does not have an Inverse.

Or A is not invertible.

Now for the given matrix A,

|A|=0

so, value of x should be

$|A|=\left|\begin{array}{cc}2&4\\8&x\end{array}\right|=0$

$8 \times 4 - 2x = 0 \\ \\ 32 - 2x = 0 \\\\ - 2x = - 32 \\ \\ 2x = 32 \\ \\ x = 16$

Thus,

if x= 16,

then matrix doesn't have an inverse.

Hope it helps you.

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