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Matrices — Maths STD 12 Science — Question

Gujarat BoardEnglish MediumSTD 12 ScienceMathsMatrices1 Mark
MCQ
If $\left[\begin{array}{cc}2 a+b & a-2 b \\ 5 c-d & 4 c+3 d\end{array}\right]=\left[\begin{array}{cc}4 & -3 \\ 11 & 24\end{array}\right]$, then value of $a+b-c+2 d$ is
  • ✓
    $8$
  • B
    $10$
  • C
    $4$
  • D
    $-8$
✓

Answer

Correct option: A.
$8$
From the definition of equality of two matrices, we have
$2 a+b=4 ....(i)$
$5 c-d=11 .....(iii)$
$a-2 b=-3.....(ii)$
$4 c+3 d=24......(iv)$
Solving $(i)$ and $(ii)$, we get
$5 a=5 \Rightarrow a=1, b=2$
Solving $(iii)$ and $(iv)$, we get
$19 c=57 \Rightarrow c=3, d=4$
$\therefore a+b-c+2 d=1+2-3+8=8$

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