Answer:
[tex] a = \boxed{1},\: b=\boxed{0}\\\\c=\boxed{0},\: d=\boxed{1}[/tex]
Step-by-step explanation:
- [tex]\begin{bmatrix} 2 & 7\\\\1 & 3\end{bmatrix}\:\begin{bmatrix} -3 & 7\\\\1 & -2\end{bmatrix}=\begin{bmatrix} a & b\\\\c & d\end{bmatrix}[/tex]
- Multiply both the matrices on left side, we find:
- [tex]\begin{bmatrix} 2(-3)+7(1) & 2(7)+7(-2)\\\\1(-3)+3(1) & 1(7)+3(-2)\end{bmatrix}=\begin{bmatrix} a & b\\\\c & d\end{bmatrix}[/tex]
- [tex]\rightarrow\begin{bmatrix} -6+7 & 14-14\\\\-3+3 & 7-6\end{bmatrix}=\begin{bmatrix} a & b\\\\c & d\end{bmatrix}[/tex]
- [tex]\rightarrow\begin{bmatrix} 1 & 0\\\\0 & 1\end{bmatrix}=\begin{bmatrix} a & b\\\\c & d\end{bmatrix}[/tex]
- Comparing the corresponding elements of both the matrices on both sides, we find:
- [tex] a = \boxed{1},\: b=\boxed{0},\:c=\boxed{0},\: d=\boxed{1}[/tex]
