91Ó°ÊÓ

Perform multiplication between the matrices that are on left side of the provided equation.

$\left[\begin{array}{cc}3â‹\dots a+5â‹\dots c& 3â‹\dots b+5â‹\dots d\\ (−1)â‹\dots a+7â‹\dots c& (−1)â‹\dots b+7â‹\dots d\end{array}\right]=\left[\begin{array}{cc}3a+5c& 3b+5d\\ −a+7c& −b+7d\end{array}\right]$

Equate the obtained matrix with the matrix on the right of provided equation.

$\left[\begin{array}{cc}3a+5c& 3b+5d\\ −a+7c& −b+7d\end{array}\right]=\left[\begin{array}{cc}3& 5\\ −1& 7\end{array}\right]$

Make two equations and extract equation for a and b from them.

$\begin{array}{c}3a+5c=3\\ 3a=−5c+3\\ a=\frac{−5c+3}{3}\end{array}$

$\begin{array}{c}3b+5d=5\\ 3b=−5d+5\\ b=\frac{−5d+5}{3}\end{array}$

Pick the equations$−a+7c=−1$and$−b+7d=7$ after it substitute the values of a and b into these equations.

$\begin{array}{c}−\left(\frac{−5c+3}{3}\right)+7c=−1\\ \frac{5c−3}{3}+7c=−1\\ c=0\end{array}$

$\begin{array}{c}−\left(\frac{−5d+5}{3}\right)+7d=7\\ \frac{5d−5}{3}+7d=7\\ d=1\end{array}$

The obtained value of c and d are 0 and 1 respectively.

Substitute the obtained value of c and d into $a=\frac{−5c+3}{3}$and$b=\frac{−5d+5}{3}$respectively then simplify.

$\begin{array}{c}a=\frac{−5â‹\dots \left(0\right)+3}{3}\\ =\frac{3}{3}\\ =1\end{array}$

$\begin{array}{c}b=\frac{−5\left(1\right)+5}{3}\\ =0\end{array}$

The obtained value of a and b are 1 and 0 respectively.

The matrix will be$\left[\begin{array}{cc}1& 0\\ 0& 1\end{array}\right]$ . As it is an identity matrix so whenever a multiplication performed between this matrix and any other matrix having 2 columns then the result will be same as that matrix with two columns.