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Matrices — Mathematics STD 10 — Question

ICSE BoardEnglish MediumSTD 10MathematicsMatrices4 Marks
Question
If $\left|\begin{array}{cc}2 a + b & c \\ d & 3 a - b \end{array}\right|=\left|\begin{array}{cc}4 & 3 a \\ 7 & 6\end{array}\right|$, find the values of $a , b , c$ and $d$.
✓

Answer

Given,
$\left|\begin{array}{cc} 2 a+b & c \\ d & 3 a-b \end{array}\right|_{2 \times 2}=\left|\begin{array}{cc} 4 & 3 a \\ 7 & 6 \end{array}\right|_{2 \times 2}$
$2 a+b=4......(1)$
$3 a-b=6......(2)$
Adding $(1)$ and $(2),$ we get
$5 a=10$
$\Rightarrow a=2$
from $(1)$
$2(2)+b=4$
$\Rightarrow b=0$
$C=3 a$
$\Rightarrow C=3 \times 2$
$\Rightarrow c=6$
$\Rightarrow d=7$

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