Question

Find the inverse of each of the matrices, if it exists\(\begin{bmatrix} 2 & 1 \\ 4 & 2 \end{bmatrix}\)

Answer 1

Let A=\(\begin{bmatrix} 2 & 1 \\ 4 & 2 \end{bmatrix}\) 

We know that A = IA 

\(\begin{bmatrix} 2 & 1 \\ 4 & 2 \end{bmatrix}\)=\(\begin{bmatrix} 1 & 0 \\ 0 & 1 \end{bmatrix}\)A 

Applying \(R_1\rightarrow R_1-\frac{1}{2}R_2\), we have: 

\(\begin{bmatrix} 0 & 0 \\ 4 & 2 \end{bmatrix}\)=\(\begin{bmatrix} 1 & -\frac12 \\ 0 & 1 \end{bmatrix}\)A 

Now, in the above equation, we can see all the zeros in the first row of the matrix on the L.H.S. Therefore, A⁻¹ does not exist.