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Matrices — Maths STD 12 Science — Question

Gujarat BoardEnglish MediumSTD 12 ScienceMathsMatrices1 Mark
MCQ
If $A=\left[\begin{array}{ll}3 & 4 \\ 5 & 2\end{array}\right]$ and $2 A+B$ is a null matrix, then $B$ is equal to:
  • A
    $\left[\begin{array}{cc}6 & 8 \\ 10 & 4\end{array}\right]$
  • B
    $\left[\begin{array}{cc}-6 & -8 \\ -10 & -4\end{array}\right]$
  • C
    $\left[\begin{array}{cc}5 & 8 \\ 10 & 3\end{array}\right]$
  • D
    $\left[\begin{array}{cc}-5 & -8 \\ -10 & -3\end{array}\right]$
✓

Answer

Given, $A=\left[\begin{array}{ll}3 & 4 \\ 5 & 2\end{array}\right]$ and $2 A+B=O=\left[\begin{array}{ll}0 & 0 \\ 0 & 0\end{array}\right]$
Let $B=\left[\begin{array}{ll}a & b \\ c & d\end{array}\right] \Rightarrow 2\left[\begin{array}{ll}3 & 4 \\ 5 & 2\end{array}\right]+\left[\begin{array}{ll}a & b \\ c & d\end{array}\right]=\left[\begin{array}{ll}0 & 0 \\ 0 & 0\end{array}\right]$
On comparing, we get
\[\begin{array}{l}
a+6=0 \Rightarrow a=-6 ; b+8=0 \Rightarrow b=-8 \\
c+10=0 \Rightarrow c=-10 \text { and } d+4=0 \Rightarrow d=-4 . \\
\therefore \quad \text { Required matrix, } B=\left[\begin{array}{cc}
-6 & -8 \\
-10 & -4
\end{array}\right]
\end{array}\]

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