Question

If $A=\left[\begin{array}{cc}3& a\\ -4& 8\end{array}\right],B=\left[\begin{array}{cc}c& 4\\ -3& 0\end{array}\right],C=\left[\begin{array}{cc}-1& 4\\ 3& b\end{array}\right]$ & $3A-2B=6C$, find the values of $a,b$ and $c.$

Answer 1

Given,

$A=\left[\begin{array}{cc}3& a\\ -4& 8\end{array}\right],B=\left[\begin{array}{cc}c& 4\\ -3& 0\end{array}\right],C=\left[\begin{array}{cc}-1& 4\\ 3& b\end{array}\right]$

$3A-2B=6C$

$\Rightarrow \left[\begin{array}{cc}9& 3a\\ -12& 24\end{array}\right]-\left[\begin{array}{cc}2c& 8\\ -6& 0\end{array}\right]=\left[\begin{array}{cc}-6& 24\\ 18& 6b\end{array}\right]$

$\Rightarrow \left[\begin{array}{cc}9-2c& 3a-8\\ -6& 24\end{array}\right]=\left[\begin{array}{cc}-6& 24\\ 18& 6b\end{array}\right]$

$24=6b\Rightarrow b=49-2c=-6\Rightarrow 9+6=2c\Rightarrow c=\frac{15}{2}3a-8=24\Rightarrow 3a=32\Rightarrow a=\frac{32}{3}$