MHT CET · Maths · Matrices
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
- A \(2,-1\)
- B 1,2
- C 2,1
- D \(-1,2\)
Answer & Solution
Correct Answer
(A) \(2,-1\)
Step-by-step Solution
Detailed explanation
\(
|A|=1 \times(7-20)-a(10-7)+3(4-2)=3 a-7
\)
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 \(\mathrm{b}=-1\)
|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 \(\mathrm{b}=-1\)
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