If $A=\left[\begin{array}{lll}1 & a & 3 \\ 1 & 1 & 5 \\ 2 & 4 & 7\end{array}\right]$ and…

If $A=\left[\begin{array}{lll}1 & a & 3 \\ 1 & 1 & 5 \\ 2 & 4 & 7\end{array}\right]$ and $A^{-1}=\left[\begin{array}{ccc}13 & 2 & -7 \\ -3 & b & 2 \\ -2 & 0 & 1\end{array}\right]$, then the values of $a$ and $b$ are respectively
  1. $2,-1$
  2. 1,2
  3. 2,1
  4. $-1,2$

Solution

$|A|=1 \times(7-20)-a(10-7)+3(4-2)=3 a-7$ Now $-3=-\left\{\frac{-3}{3 a-7}\right\} \Rightarrow a=2$ Also $\mathrm{b}=\frac{7-6}{3 \mathrm{a}-7}=\frac{1}{3 \times 2-7}=-1$ Hence $\mathrm{a}=2$ and $\mathrm{b}=-1$

Asked in: MHT CET 2022 (06 Aug Shift 1)

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