Question

What is "a" if B=
is a singular matrix
| 2
2 a​

Answer 1

The value of a=4

Explanation:

Given the matrix

`B=\begin{pmatrix}1\:&\:2\:\\ \:\:\:2\:&\:a\end{pmatrix}`

• A matrix is singular if its determinent is zero.

so solving the matrix B by taking its determinant to get the value a

`\det \begin{pmatrix}1&2\\ 2&a\end{pmatrix}=0`

as according to determinant formula

`\det \begin{pmatrix}a\:&\:b\:\\ c\:&\:d\:\end{pmatrix}\:=\:ad-bc`

`1\cdot \:a-2\cdot \:2=0`

`a-4=0`

`a=4`

Therefore, the value of a=4