Given that A = [ ll 3 & 0 0 & 4 ] and B = [ ll a & b 0 & c ] and … - Vidyadip

Question

Given that $A =\left[\begin{array}{ll}3 & 0 \\ 0 & 4\end{array}\right]$ and $B = \left[\begin{array}{ll}a & b \\ 0 & c\end{array}\right]$ and that $AB = A + B,$ find the values of $a, b$ and $c.$

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Answer

$AB = A + B$
$\begin{array}{l}{\left[\begin{array}{ll}3 & 0 \\ 0 & 4\end{array}\right]\left[\begin{array}{ll}a & b \\ 0 & c\end{array}\right]=\left[\begin{array}{ll}3 & 0 \\ 0 & 4\end{array}\right]+\left[\begin{array}{ll}a & b \\ 0 & c\end{array}\right]} \end{array} $
$ {\left[\begin{array}{cc}3 a & 3 b \\ 0 & 4 c\end{array}\right]=\left[\begin{array}{cc}3+a & b \\ 0 & 4+c\end{array}\right]}$
$3 a=3+a$
$2 a=3$
$a=\frac{3}{2}$
$3 b=b$
$2 b=0$
$b=0$
$4 c=4+c$
$3 c=4$
$c=\frac{4}{3} .$

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