Adjoint and Inverse of Matrices
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Matrix and Determinant

78904 If \(B=\left[\begin{array}{ccc}5 & 2 \alpha & 1 \\ 0 & 2 & 1 \\ \alpha & 3 & -1\end{array}\right]\) is the inverse of a \(3 \times 3\) matrix \(A\), then the sum of all values of \(\alpha\) for which \(\operatorname{det}(\mathrm{A})+\mathbf{1}=\mathbf{0}\), is

1 0
2 -1
3 1
4 2
JEE Main-2019-12.04.2019
Matrix and Determinant

78905 If \(A=\left[\begin{array}{cc}\cos \theta & -\sin \theta \\ \sin \theta & \cos \theta\end{array}\right]\), then the matrix \(A^{-50}\) when \(\theta=\frac{\pi}{12}\), is equal to

1 \(\left[\begin{array}{cc}\frac{1}{2} & \frac{\sqrt{3}}{2} \\ -\frac{\sqrt{3}}{2} & \frac{1}{2}\end{array}\right]\)
2 \(\left[\begin{array}{cc}\frac{\sqrt{3}}{2} & \frac{1}{2} \\ -\frac{1}{2} & \frac{\sqrt{3}}{2}\end{array}\right]\)
3 \(\left[\begin{array}{cc}\frac{\sqrt{3}}{2} & \frac{1}{2} \\ -\frac{1}{2} & \frac{\sqrt{3}}{2}\end{array}\right]\)
4 \(\left[\begin{array}{cc}\frac{1}{2} & -\frac{\sqrt{3}}{2} \\ \frac{\sqrt{3}}{2} & \frac{1}{2}\end{array}\right]\)
JEE Main-2019-09.01.2019
Matrix and Determinant

78906 If \(A=\left[\begin{array}{cc}2 & -3 \\ -4 & 1\end{array}\right]\), then adj \(\left(3 A^{2}+12 A\right)\) is equal to

1 \(\left[\begin{array}{cc}72 & -84 \\ -63 & 51\end{array}\right]\)
2 \(\left[\begin{array}{ll}51 & 63 \\ 84 & 72\end{array}\right]\)
3 \(\left[\begin{array}{ll}51 & 84 \\ 63 & 72\end{array}\right]\)
4 \(\left[\begin{array}{cc}72 & -63 \\ -84 & 51\end{array}\right]\)
JEE Main-2021
Matrix and Determinant

78907 If \(A=\left[\begin{array}{cc}5 a & -b \\ 3 & 2\end{array}\right]\) and \(A\) adj \(A=A A^{T}\), then \(5 a+\) \(b\) is equal to

1 -1
2 5
3 4
4 13
JEE Main-2021
Join With Us for More Updates
Matrix and Determinant

78904 If \(B=\left[\begin{array}{ccc}5 & 2 \alpha & 1 \\ 0 & 2 & 1 \\ \alpha & 3 & -1\end{array}\right]\) is the inverse of a \(3 \times 3\) matrix \(A\), then the sum of all values of \(\alpha\) for which \(\operatorname{det}(\mathrm{A})+\mathbf{1}=\mathbf{0}\), is

1 0
2 -1
3 1
4 2
JEE Main-2019-12.04.2019
Matrix and Determinant

78905 If \(A=\left[\begin{array}{cc}\cos \theta & -\sin \theta \\ \sin \theta & \cos \theta\end{array}\right]\), then the matrix \(A^{-50}\) when \(\theta=\frac{\pi}{12}\), is equal to

1 \(\left[\begin{array}{cc}\frac{1}{2} & \frac{\sqrt{3}}{2} \\ -\frac{\sqrt{3}}{2} & \frac{1}{2}\end{array}\right]\)
2 \(\left[\begin{array}{cc}\frac{\sqrt{3}}{2} & \frac{1}{2} \\ -\frac{1}{2} & \frac{\sqrt{3}}{2}\end{array}\right]\)
3 \(\left[\begin{array}{cc}\frac{\sqrt{3}}{2} & \frac{1}{2} \\ -\frac{1}{2} & \frac{\sqrt{3}}{2}\end{array}\right]\)
4 \(\left[\begin{array}{cc}\frac{1}{2} & -\frac{\sqrt{3}}{2} \\ \frac{\sqrt{3}}{2} & \frac{1}{2}\end{array}\right]\)
JEE Main-2019-09.01.2019
Matrix and Determinant

78906 If \(A=\left[\begin{array}{cc}2 & -3 \\ -4 & 1\end{array}\right]\), then adj \(\left(3 A^{2}+12 A\right)\) is equal to

1 \(\left[\begin{array}{cc}72 & -84 \\ -63 & 51\end{array}\right]\)
2 \(\left[\begin{array}{ll}51 & 63 \\ 84 & 72\end{array}\right]\)
3 \(\left[\begin{array}{ll}51 & 84 \\ 63 & 72\end{array}\right]\)
4 \(\left[\begin{array}{cc}72 & -63 \\ -84 & 51\end{array}\right]\)
JEE Main-2021
Matrix and Determinant

78907 If \(A=\left[\begin{array}{cc}5 a & -b \\ 3 & 2\end{array}\right]\) and \(A\) adj \(A=A A^{T}\), then \(5 a+\) \(b\) is equal to

1 -1
2 5
3 4
4 13
JEE Main-2021
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Matrix and Determinant

78904 If \(B=\left[\begin{array}{ccc}5 & 2 \alpha & 1 \\ 0 & 2 & 1 \\ \alpha & 3 & -1\end{array}\right]\) is the inverse of a \(3 \times 3\) matrix \(A\), then the sum of all values of \(\alpha\) for which \(\operatorname{det}(\mathrm{A})+\mathbf{1}=\mathbf{0}\), is

1 0
2 -1
3 1
4 2
JEE Main-2019-12.04.2019
Matrix and Determinant

78905 If \(A=\left[\begin{array}{cc}\cos \theta & -\sin \theta \\ \sin \theta & \cos \theta\end{array}\right]\), then the matrix \(A^{-50}\) when \(\theta=\frac{\pi}{12}\), is equal to

1 \(\left[\begin{array}{cc}\frac{1}{2} & \frac{\sqrt{3}}{2} \\ -\frac{\sqrt{3}}{2} & \frac{1}{2}\end{array}\right]\)
2 \(\left[\begin{array}{cc}\frac{\sqrt{3}}{2} & \frac{1}{2} \\ -\frac{1}{2} & \frac{\sqrt{3}}{2}\end{array}\right]\)
3 \(\left[\begin{array}{cc}\frac{\sqrt{3}}{2} & \frac{1}{2} \\ -\frac{1}{2} & \frac{\sqrt{3}}{2}\end{array}\right]\)
4 \(\left[\begin{array}{cc}\frac{1}{2} & -\frac{\sqrt{3}}{2} \\ \frac{\sqrt{3}}{2} & \frac{1}{2}\end{array}\right]\)
JEE Main-2019-09.01.2019
Matrix and Determinant

78906 If \(A=\left[\begin{array}{cc}2 & -3 \\ -4 & 1\end{array}\right]\), then adj \(\left(3 A^{2}+12 A\right)\) is equal to

1 \(\left[\begin{array}{cc}72 & -84 \\ -63 & 51\end{array}\right]\)
2 \(\left[\begin{array}{ll}51 & 63 \\ 84 & 72\end{array}\right]\)
3 \(\left[\begin{array}{ll}51 & 84 \\ 63 & 72\end{array}\right]\)
4 \(\left[\begin{array}{cc}72 & -63 \\ -84 & 51\end{array}\right]\)
JEE Main-2021
Matrix and Determinant

78907 If \(A=\left[\begin{array}{cc}5 a & -b \\ 3 & 2\end{array}\right]\) and \(A\) adj \(A=A A^{T}\), then \(5 a+\) \(b\) is equal to

1 -1
2 5
3 4
4 13
JEE Main-2021
NEET DIGITAL LIBRARY
Matrix and Determinant

78904 If \(B=\left[\begin{array}{ccc}5 & 2 \alpha & 1 \\ 0 & 2 & 1 \\ \alpha & 3 & -1\end{array}\right]\) is the inverse of a \(3 \times 3\) matrix \(A\), then the sum of all values of \(\alpha\) for which \(\operatorname{det}(\mathrm{A})+\mathbf{1}=\mathbf{0}\), is

1 0
2 -1
3 1
4 2
JEE Main-2019-12.04.2019
Matrix and Determinant

78905 If \(A=\left[\begin{array}{cc}\cos \theta & -\sin \theta \\ \sin \theta & \cos \theta\end{array}\right]\), then the matrix \(A^{-50}\) when \(\theta=\frac{\pi}{12}\), is equal to

1 \(\left[\begin{array}{cc}\frac{1}{2} & \frac{\sqrt{3}}{2} \\ -\frac{\sqrt{3}}{2} & \frac{1}{2}\end{array}\right]\)
2 \(\left[\begin{array}{cc}\frac{\sqrt{3}}{2} & \frac{1}{2} \\ -\frac{1}{2} & \frac{\sqrt{3}}{2}\end{array}\right]\)
3 \(\left[\begin{array}{cc}\frac{\sqrt{3}}{2} & \frac{1}{2} \\ -\frac{1}{2} & \frac{\sqrt{3}}{2}\end{array}\right]\)
4 \(\left[\begin{array}{cc}\frac{1}{2} & -\frac{\sqrt{3}}{2} \\ \frac{\sqrt{3}}{2} & \frac{1}{2}\end{array}\right]\)
JEE Main-2019-09.01.2019
Matrix and Determinant

78906 If \(A=\left[\begin{array}{cc}2 & -3 \\ -4 & 1\end{array}\right]\), then adj \(\left(3 A^{2}+12 A\right)\) is equal to

1 \(\left[\begin{array}{cc}72 & -84 \\ -63 & 51\end{array}\right]\)
2 \(\left[\begin{array}{ll}51 & 63 \\ 84 & 72\end{array}\right]\)
3 \(\left[\begin{array}{ll}51 & 84 \\ 63 & 72\end{array}\right]\)
4 \(\left[\begin{array}{cc}72 & -63 \\ -84 & 51\end{array}\right]\)
JEE Main-2021
Matrix and Determinant

78907 If \(A=\left[\begin{array}{cc}5 a & -b \\ 3 & 2\end{array}\right]\) and \(A\) adj \(A=A A^{T}\), then \(5 a+\) \(b\) is equal to

1 -1
2 5
3 4
4 13
JEE Main-2021
Join With Us for More Updates