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GUJCET · Maths · Matrices
If \(A=\left[\begin{array}{lll}4 & 0 & 0 \\ 0 & 3 & 0 \\ 0 & 0 & 2\end{array}\right]\) and \(B=\left[\begin{array}{lll}1 & 0 & 0 \\ 0 & 2 & 0 \\ 0 & 0 & 3\end{array}\right]\) then, \((A+B)^{-1}=\) ____________ .
- A \(\frac{1}{25} l _2\)
- B \(\frac{1}{5} I _3\)
- C \(-\frac{1}{5} I _3\)
- D \(-\frac{1}{25} I _3\),
Answer & Solution
Correct Answer
(B) \(\frac{1}{5} I _3\)
Step-by-step Solution
Detailed explanation
\(A+B = \left[\begin{array}{lll}4+1 & 0 & 0 \\ 0 & 3+2 & 0 \\ 0 & 0 & 2+3\end{array}\right] = \left[\begin{array}{lll}5 & 0 & 0 \\ 0 & 5 & 0 \\ 0 & 0 & 5\end{array}\right]\) \((A+B)^{-1} = \left(5\left[\begin{array}{lll}1 & 0 & 0 \\ 0 & 1 & 0 \\ 0 & 0 & 1\end{array}\right]\right)^{-1} = \frac{1}{5}\left[\begin{array}{lll}1 & 0 & 0 \\ 0 & 1 & 0 \\ 0 & 0 & 1\end{array}\right] = \frac{1}{5} I_3\)
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