If A = | cc p & q 8 & 5 |, B = | cc 3 p & 5 q 2 q & 7 | and if A … - Vidyadip

Question

If $A =\left|\begin{array}{cc} p & q \\ 8 & 5\end{array}\right|, B =\left|\begin{array}{cc}3 p & 5 q \\ 2 q & 7\end{array}\right|$ and if $A + B =\left|\begin{array}{cc}12 & 6 \\ 2 r & 3 s \end{array}\right|$, find the values of $p , q , r$ and $s$.

✓

Answer

$\begin{array}{l}\left|\begin{array}{ll}3 a+2 b & 2 a-b \\ 4 p-3 q & 2 p+q\end{array}\right|=\left|\begin{array}{ll}12 & 1 \\ 16 & 8\end{array}\right| \end{array}$
$3 a+2 b=12 ........(1)$
$2 a-b=1 ......(2)$
$b=2 a-1$
$4 p-3 q=16 .......(3)$
$2 p+q=8......(4)$
putting the value of $b$ in $(1)$
$3 a+4 a-2=12$
$7 a=14$
$a=2$
from $(2)$
$4-b=1$
$b=3$
putting the value of $q$ in $(3)$
$4 p-24+6 p=16$
$10 p=40$
$p=4$
from$(4)$
$8+q=8$
$q=0$

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