Question: If matrix $A = \begin{bmatrix} 3 & 2 & 4 \\ 1 & 2 & - 1 \\ 0 & 1 & 1 \end{bmatrix}$and \(A^{- 1} =...

Question

If matrix $A = \begin{bmatrix} 3 & 2 & 4 \\ 1 & 2 & - 1 \\ 0 & 1 & 1 \end{bmatrix}$ and $A^{- 1} = \frac{1}{K}adj(A)$ , then K is

Answer 1

We know that $A^{- 1} = \frac{adj(A)}{|A|}$ . We have $A^{- 1} = \frac{1}{K}adj(A)$ i.e.

$K = |A|$

and $K = \left| \begin{matrix} 3 & 2 & 4 \\ 1 & 2 & - 1 \\ 0 & 1 & 1 \end{matrix} \right|$ $= 3(3) - 2(1) + 4(1) = 9 - 2 + 4 = 11$

Question: If matrix \(A = \begin{bmatrix} 3 & 2 & 4 \\ 1 & 2 & - 1 \\ 0 & 1 & 1 \end{bmatrix}\)and \(A^{- 1} =...