Question

Find the inverse of the matrices by using elementary row transformations \(\begin{bmatrix} 2 & 0& -1\\[0.3em] 5&1 & 0 \\0 & 1& 3\end{bmatrix}\).

Answer 1

From the row transformation

A = IA

On applying R₁ → (1/2)R₁

On applying R₂ → R₂ - 5R₁

On applying R₃ → R₃ - R₂

On applying R₃ → 2R₃ 

On applying R₁ → R₁ + (1/2)R₃ and R₂ → R₂ - (5/2)R₃

As we know

I = A^-1 A

So