Obtain the inverse of the following matrix using elementary operation:
$A = ⎡ ⎢ ⎣ \begin{matrix} 3 & 0 & - 1 2 & 3 & 0 0 & 4 & 1 \end{matrix} ⎤ ⎥ ⎦$

⎡ ⎢ ⎣ \begin{matrix} - 3 & - 4 & - 3 2 & 3 & - 2 8 & - 12 & 9 \end{matrix} ⎤ ⎥ ⎦

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⎡ ⎢ ⎣ \begin{matrix} 3 & 4 & 3 2 & 3 & - 2 8 & - 12 & 9 \end{matrix} ⎤ ⎥ ⎦

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⎡ ⎢ ⎣ \begin{matrix} - 3 & - 4 & 3 2 & 3 & - 2 - 8 & - 12 & 9 \end{matrix} ⎤ ⎥ ⎦

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⎡ ⎢ ⎣ \begin{matrix} 3 & - 2 & 8 - 4 & 3 & - 12 3 & - 2 & 9 \end{matrix} ⎤ ⎥ ⎦

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Solution

The correct option is A $⎡ ⎢ ⎣ \begin{matrix} 3 & - 2 & 8 - 4 & 3 & - 12 3 & - 2 & 9 \end{matrix} ⎤ ⎥ ⎦$
GIven $A = ⎡ ⎢ ⎣ \begin{matrix} 3 & 0 & - 1 2 & 3 & 0 0 & 4 & 1 \end{matrix} ⎤ ⎥ ⎦$

Therefore, $A^{- 1} = \frac{1}{| A |} a d j (A)$

$⟹ A^{- 1} = \frac{1}{3 (3 - 0) - 1 (8 - 0)} ⎡ ⎢ ⎣ \begin{matrix} 3 & - 2 & 8 - 4 & 3 & - 12 3 & - 2 & 9 \end{matrix} ⎤ ⎥ ⎦$

$⟹ A^{- 1} = ⎡ ⎢ ⎣ \begin{matrix} 3 & - 2 & 8 - 4 & 3 & - 12 3 & - 2 & 9 \end{matrix} ⎤ ⎥ ⎦$

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Similar questions

Q. Obtain the inverse of the following matrix using elementary operations:

A = ⎡ ⎢ ⎣ \begin{matrix} 0 & 1 & 2 1 & 2 & 3 3 & 1 & 1 \end{matrix} ⎤ ⎥ ⎦

If such that f(2) = 0, then f(x) is

(A) (B)

Find the following integrals.
If $\frac{d}{d x} f (x) = 4 x^{3} - \frac{3}{x^{4}}$ such that f(2)=0. Then f(x)is
$(a) x^{4} + \frac{1}{x^{3}} - \frac{129}{8} (b) x^{3} + \frac{1}{x^{4}} + \frac{129}{8} (c) x^{4} + \frac{1}{x^{3}} + \frac{129}{8} (d) x^{3} + \frac{1}{x^{4}} - \frac{129}{8}$

Q. Evaluate

129 - (129 - (130 - 30))

Q. Find the inverse of the following matrix using elementary operations.

A

⎡ ⎢ ⎣ \begin{matrix} 1 & 2 & - 2 - 1 & 3 & 0 0 & - 2 & 1 \end{matrix} ⎤ ⎥ ⎦

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Obtain the inverse of the following matrix using elementary operation:A=⎡⎢⎣30−1230041⎤⎥⎦

The correct option is A ⎡⎢⎣3−28−43−123−29⎤⎥⎦GIven A=⎡⎢⎣30−1230041⎤⎥⎦Therefore, A−1=1|A|adj(A)⟹A−1=13(3−0)−1(8−0)⎡⎢⎣3−28−43−123−29⎤⎥⎦⟹A−1=⎡⎢⎣3−28−43−123−29⎤⎥⎦

Obtain the inverse of the following matrix using elementary operation:
$A = ⎡ ⎢ ⎣ \begin{matrix} 3 & 0 & - 1 2 & 3 & 0 0 & 4 & 1 \end{matrix} ⎤ ⎥ ⎦$