Given : \(\begin{bmatrix}
5 & -7 \\[0.3em]
-2 & 3 \\[0.3em]
\end{bmatrix}\). A = \(\begin{bmatrix}
-16 & -6 \\[0.3em]
7 & 2 \\[0.3em]
\end{bmatrix}.\)
To find : matrix A
Formula used :
Where cij = ai1b1j + ai2b2j + ai3b3j + ……………… + ainbnj
IF XA = B, then A = X -1B
Determinant of given matrix = \(\begin{bmatrix}
5 &-7 \\[0.3em]
-2&3 \\[0.3em]
\end{bmatrix}\) = 5(3) – (-7)(-2) = 15 – 14 = 1
A = \(\begin{bmatrix}
1 & -4 \\[0.3em]
3 & -6 \\[0.3em]
\end{bmatrix}\)
A = \(\begin{bmatrix}
1 & -4 \\[0.3em]
3 & -6 \\[0.3em]
\end{bmatrix}\)