Adjoint and Inverse of Matrices
Matrix and Determinant

78888 If \(A=\left[\begin{array}{ccc}1 & 0 & -2 \\ -2 & -1 & 2 \\ 3 & 4 & 1\end{array}\right]\), then \(A^{-1}=\)

1 \(\mathrm{A}^{2}-2 \mathrm{~A}-4 \mathrm{I}\)
2 \(A^{2}-A-3 I\)
3 \(\frac{1}{2}\left[\mathrm{~A}^{2}+\mathrm{A}+2 \mathrm{I}\right]\)
4 \(\mathrm{A}^{2}+\mathrm{A}-2 \mathrm{I}\)
Matrix and Determinant

78889 If \(\mathrm{A}=\left[\begin{array}{ccc} \mathbf{k} / \mathbf{2} & \mathbf{0} & \mathbf{0} \\ \mathbf{0} & \mathbf{l / 3} & \mathbf{0} \\ \mathbf{0} & \mathbf{0} & \mathbf{m} / \mathbf{4} \end{array}\right] \text { and }\)
\(\quad \mathrm{A}^{-\mathbf{1}}=\left[\begin{array}{ccc} \mathbf{1} / \mathbf{2} & \mathbf{0} & \mathbf{0} \\ \mathbf{0} & \mathbf{1} / \mathbf{3} & \mathbf{0} \\ \mathbf{0} & \mathbf{0} & \mathbf{1} / \mathbf{4} \end{array}\right] \text {, then } \mathbf{k}+\mathbf{l}+\mathbf{m}=\)
and

1 1
2 9
3 14
4 29
Matrix and Determinant

78890 For the matrix \(A=\left[\begin{array}{lll}3 & -3 & 4 \\ 2 & -3 & 4 \\ 0 & -1 & 1\end{array}\right], A^{-1}=\)

1 \(\mathrm{A}\)
2 \(A^{2}\)
3 \(\mathrm{A}^{3}\)
4 \(\mathrm{A}^{4}\)
Matrix and Determinant

78891 If \(A=\left(\begin{array}{ccc}5 & 5 x & x \\ 0 & x & 5 x \\ 0 & 0 & 5\end{array}\right)\) and \(\left|A^{2}\right|=25\), then \(|x|\) is equal to

1 \(\frac{1}{5}\)
2 5
3 \(5^{2}\)
4 1
Matrix and Determinant

78888 If \(A=\left[\begin{array}{ccc}1 & 0 & -2 \\ -2 & -1 & 2 \\ 3 & 4 & 1\end{array}\right]\), then \(A^{-1}=\)

1 \(\mathrm{A}^{2}-2 \mathrm{~A}-4 \mathrm{I}\)
2 \(A^{2}-A-3 I\)
3 \(\frac{1}{2}\left[\mathrm{~A}^{2}+\mathrm{A}+2 \mathrm{I}\right]\)
4 \(\mathrm{A}^{2}+\mathrm{A}-2 \mathrm{I}\)
Matrix and Determinant

78889 If \(\mathrm{A}=\left[\begin{array}{ccc} \mathbf{k} / \mathbf{2} & \mathbf{0} & \mathbf{0} \\ \mathbf{0} & \mathbf{l / 3} & \mathbf{0} \\ \mathbf{0} & \mathbf{0} & \mathbf{m} / \mathbf{4} \end{array}\right] \text { and }\)
\(\quad \mathrm{A}^{-\mathbf{1}}=\left[\begin{array}{ccc} \mathbf{1} / \mathbf{2} & \mathbf{0} & \mathbf{0} \\ \mathbf{0} & \mathbf{1} / \mathbf{3} & \mathbf{0} \\ \mathbf{0} & \mathbf{0} & \mathbf{1} / \mathbf{4} \end{array}\right] \text {, then } \mathbf{k}+\mathbf{l}+\mathbf{m}=\)
and

1 1
2 9
3 14
4 29
Matrix and Determinant

78890 For the matrix \(A=\left[\begin{array}{lll}3 & -3 & 4 \\ 2 & -3 & 4 \\ 0 & -1 & 1\end{array}\right], A^{-1}=\)

1 \(\mathrm{A}\)
2 \(A^{2}\)
3 \(\mathrm{A}^{3}\)
4 \(\mathrm{A}^{4}\)
Matrix and Determinant

78891 If \(A=\left(\begin{array}{ccc}5 & 5 x & x \\ 0 & x & 5 x \\ 0 & 0 & 5\end{array}\right)\) and \(\left|A^{2}\right|=25\), then \(|x|\) is equal to

1 \(\frac{1}{5}\)
2 5
3 \(5^{2}\)
4 1
Matrix and Determinant

78888 If \(A=\left[\begin{array}{ccc}1 & 0 & -2 \\ -2 & -1 & 2 \\ 3 & 4 & 1\end{array}\right]\), then \(A^{-1}=\)

1 \(\mathrm{A}^{2}-2 \mathrm{~A}-4 \mathrm{I}\)
2 \(A^{2}-A-3 I\)
3 \(\frac{1}{2}\left[\mathrm{~A}^{2}+\mathrm{A}+2 \mathrm{I}\right]\)
4 \(\mathrm{A}^{2}+\mathrm{A}-2 \mathrm{I}\)
Matrix and Determinant

78889 If \(\mathrm{A}=\left[\begin{array}{ccc} \mathbf{k} / \mathbf{2} & \mathbf{0} & \mathbf{0} \\ \mathbf{0} & \mathbf{l / 3} & \mathbf{0} \\ \mathbf{0} & \mathbf{0} & \mathbf{m} / \mathbf{4} \end{array}\right] \text { and }\)
\(\quad \mathrm{A}^{-\mathbf{1}}=\left[\begin{array}{ccc} \mathbf{1} / \mathbf{2} & \mathbf{0} & \mathbf{0} \\ \mathbf{0} & \mathbf{1} / \mathbf{3} & \mathbf{0} \\ \mathbf{0} & \mathbf{0} & \mathbf{1} / \mathbf{4} \end{array}\right] \text {, then } \mathbf{k}+\mathbf{l}+\mathbf{m}=\)
and

1 1
2 9
3 14
4 29
Matrix and Determinant

78890 For the matrix \(A=\left[\begin{array}{lll}3 & -3 & 4 \\ 2 & -3 & 4 \\ 0 & -1 & 1\end{array}\right], A^{-1}=\)

1 \(\mathrm{A}\)
2 \(A^{2}\)
3 \(\mathrm{A}^{3}\)
4 \(\mathrm{A}^{4}\)
Matrix and Determinant

78891 If \(A=\left(\begin{array}{ccc}5 & 5 x & x \\ 0 & x & 5 x \\ 0 & 0 & 5\end{array}\right)\) and \(\left|A^{2}\right|=25\), then \(|x|\) is equal to

1 \(\frac{1}{5}\)
2 5
3 \(5^{2}\)
4 1
NEET Test Series from KOTA - 10 Papers In MS WORD WhatsApp Here
Matrix and Determinant

78888 If \(A=\left[\begin{array}{ccc}1 & 0 & -2 \\ -2 & -1 & 2 \\ 3 & 4 & 1\end{array}\right]\), then \(A^{-1}=\)

1 \(\mathrm{A}^{2}-2 \mathrm{~A}-4 \mathrm{I}\)
2 \(A^{2}-A-3 I\)
3 \(\frac{1}{2}\left[\mathrm{~A}^{2}+\mathrm{A}+2 \mathrm{I}\right]\)
4 \(\mathrm{A}^{2}+\mathrm{A}-2 \mathrm{I}\)
Matrix and Determinant

78889 If \(\mathrm{A}=\left[\begin{array}{ccc} \mathbf{k} / \mathbf{2} & \mathbf{0} & \mathbf{0} \\ \mathbf{0} & \mathbf{l / 3} & \mathbf{0} \\ \mathbf{0} & \mathbf{0} & \mathbf{m} / \mathbf{4} \end{array}\right] \text { and }\)
\(\quad \mathrm{A}^{-\mathbf{1}}=\left[\begin{array}{ccc} \mathbf{1} / \mathbf{2} & \mathbf{0} & \mathbf{0} \\ \mathbf{0} & \mathbf{1} / \mathbf{3} & \mathbf{0} \\ \mathbf{0} & \mathbf{0} & \mathbf{1} / \mathbf{4} \end{array}\right] \text {, then } \mathbf{k}+\mathbf{l}+\mathbf{m}=\)
and

1 1
2 9
3 14
4 29
Matrix and Determinant

78890 For the matrix \(A=\left[\begin{array}{lll}3 & -3 & 4 \\ 2 & -3 & 4 \\ 0 & -1 & 1\end{array}\right], A^{-1}=\)

1 \(\mathrm{A}\)
2 \(A^{2}\)
3 \(\mathrm{A}^{3}\)
4 \(\mathrm{A}^{4}\)
Matrix and Determinant

78891 If \(A=\left(\begin{array}{ccc}5 & 5 x & x \\ 0 & x & 5 x \\ 0 & 0 & 5\end{array}\right)\) and \(\left|A^{2}\right|=25\), then \(|x|\) is equal to

1 \(\frac{1}{5}\)
2 5
3 \(5^{2}\)
4 1