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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
  • A
    8
  • B
    10
  • C
    4
  • D
    -8
✓

Answer

From the definition of equality of two matrices, we have
$
\begin{array}{l}
2 a+b=4 ....(i)\\
5 c-d=11 .....(iii)
\end{array}
$ $
\begin{array}{l}
a-2 b=-3.....(ii) \\

4 c+3 d=24......(iv)
\end{array}
$
Solving (i) and (ii), we get
$
5 a=5 \Rightarrow a=1, b=2
$
Solving (iii) and (iv), we get
$
\begin{aligned}
& 19 c=57 \Rightarrow c=3, d=4 \\
\therefore \quad & a+b-c+2 d=1+2-3+8=8
\end{aligned}
$

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