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Labeen Chandra Varma
Asked: 2022-11-03T01:40:05+05:30 In:

If the A = \(\begin{bmatrix} -1& 3 \\ 4 & -2 \end{bmatrix}\) satisfies equation A2 + 3A – 10I = 0, find A-1.
1. \({1\over10}\begin{bmatrix} -2& -3 \\ 4 & 1 \end{bmatrix}\)
2. \({1\over10}\begin{bmatrix} -2& 3 \\ 4 & -1 \end{bmatrix}\)
3. \({1\over10}\begin{bmatrix} 2& 3 \\ 4 & 1 \end{bmatrix}\)
4. \({1\over10}\begin{bmatrix} 2& -3 \\ -4 & 1 \end{bmatrix}\)

If the A = \(\begin{bmatrix} -1& 3 \\ 4 & -2 \end{bmatrix}\) satisfies equation A2 + 3A – 10I = 0, find A-1.
1. \({1\over10}\begin{bmatrix} -2& -3 \\ 4 & 1 \end{bmatrix}\)
2. \({1\over10}\begin{bmatrix} -2& 3 \\ 4 & -1 \end{bmatrix}\)
3. \({1\over10}\begin{bmatrix} 2& 3 \\ 4 & 1 \end{bmatrix}\)
4. \({1\over10}\begin{bmatrix} 2& -3 \\ -4 & 1 \end{bmatrix}\)
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1 Answer

  1. Correct Answer – Option 3 : \({1\over10}\begin{bmatrix} 2& 3 \\ 4 & 1 \end{bmatrix}\)

    Calculation:

    Given A satisfies the equation 

    A2 + 3A – 10I = 0

    Multiply the equation by A-1

    ⇒ A-1A2 + 3 A-1A – 10A-1I = 0

    ⇒ A + 3I – 10 A-1 = 0

    ⇒ \(\begin{bmatrix} -1& 3 \\ 4 & -2 \end{bmatrix}\) + 3 \(\begin{bmatrix} 1&0 \\ 0 & 1 \end{bmatrix}\) – 10 A-1 = \(\begin{bmatrix} 0& 0 \\ 0 & 0 \end{bmatrix}\)

    ⇒ \(\begin{bmatrix} -1+3&3+0\\4+0&-2+3\end{bmatrix}\) = 10 A-1

    ⇒ A-1 = \({1\over10}\begin{bmatrix} 2& 3 \\ 4 & 1 \end{bmatrix}\)

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