Question

If $\left[\begin{array}{cc}r+4& 6\\ 3& r+3\end{array}\right]=\left[\begin{array}{cc}& r+2\\ r+5& 4\end{array}\right]$ then $r=?$

• A. $1$
• B. $2$
• C. $3$
• D. $-1$

Answer 1

The correct option is A $1$

Given,

$\left(\begin{array}{cc}r+4& 6\\ 3& r+3\end{array}\right)={\left(\begin{array}{cc}5& r+2\\ r+5& 4\end{array}\right)}^r$

lets try at r=1

$LHS=\left(\begin{array}{cc}1+4& 6\\ 3& 1+3\end{array}\right)=\left(\begin{array}{cc}5& 6\\ 3& 4\end{array}\right)-\left(1\right)$

$(RHS{)}^{\prime }=(\left(\begin{array}{cc}5& 1+2\\ 1+5& 4\end{array}\right){)}^{\prime }=\left(\begin{array}{cc}5& 6\\ 3& 4\end{array}\right)-\left(2\right)$

From eqs.(1) and (2)

$LHS=RHS$

So $r=1$