Q71 / 170 · Manipal (MET) 2021 · Mathematics

If $\left[\begin{array}{rrr}a & 2 & 3 \\ b & 5 & -1\end{array}\right] \times\left[\begin{array}{rr}1 & 2 \\ 3 & 4 \\ -1 & 1\end{array}\right]=\left[\begin{array}{rr}4 & 13 \\ 12 & 11\end{array}\right],(a, b)$ is

  • A
    $(1,-2)$
  • B
    $(-1,-4)$
  • C
    $(1,3)$
  • Correct answer
    D
    $(1,-4)$

Solution

$\begin{aligned} & \quad\left[\begin{array}{ccc}a & 2 & 3 \\ b & 5 & -1\end{array}\right]\left[\begin{array}{cc}1 & 2 \\ 3 & 4 \\ -1 & 1\end{array}\right]=\left[\begin{array}{cc}a+6-3 & 2 a+8+3 \\ b+15+1 & 2 b+20-1\end{array}\right] \\ & \Rightarrow\left[\begin{array}{ll}a+3 & 2 a+11 \\ b+16 & 2 b+19\end{array}\right]=\left[\begin{array}{cc}4 & 13 \\ 12 & 11\end{array}\right] \text { (given) } \\ & \Rightarrow \quad a+3=4 \Rightarrow a=1 \\ & \text { and } b+16=12 \Rightarrow b=12-16=-4 \\ & \therefore \quad(a, b)=(1,-4)\end{aligned}$

Hence, the correct answer is option: 'D'.

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