Adjoint and Inverse of Matrices
Matrix and Determinant

78917 The value of \(t\) such that the matrix
\(\left(\begin{array}{ccc}1 & 3 & 2 \\ 2 & 5 & t \\ 4 & 7-t & -6\end{array}\right)\) has no inverse, are

1 3,2
2 \(3,-2\)
3 \(-3,2\)
4 \(-3,-2\)
Matrix and Determinant

78918 If \(\left(\begin{array}{ccc}5 & a & -7 \\ b & -7 & c \\ -7 & d & -1\end{array}\right)\) is the adjoint of the matrix
\(\left(\begin{array}{lll}1 & 2 & 3 \\ 2 & 3 & 1 \\ 3 & 1 & 2\end{array}\right)\), then \(\mathbf{a}+\mathbf{b}+\mathbf{c}+\mathbf{d}=\)

1 8
2 10
3 0
4 2
Matrix and Determinant

78919 If \(A=\left[\begin{array}{ccc}1 & -2 & 2 \\ 2 & -6 & 5 \\ 5 & 0 & 4\end{array}\right]\) then Adj \(A=\)

1 \(\left[\begin{array}{ccc}-24 & 8 & 2 \\ 17 & -6 & -1 \\ 30 & -10 & 2\end{array}\right]\)
2 \(\left[\begin{array}{ccc}-24 & 8 & 2 \\ 17 & -6 & 1 \\ -30 & -10 & -2\end{array}\right]\)
3 \(\left[\begin{array}{ccc}-24 & 8 & 2 \\ 17 & -6 & -1 \\ 30 & -10 & -2\end{array}\right]\)
4 \(\left[\begin{array}{ccc}24 & -8 & 2 \\ -17 & -6 & 1 \\ 30 & -10 & -2\end{array}\right]\)
Matrix and Determinant

78920 Let \(A=\left[\begin{array}{ccc}0 & 0 & -1 \\ 0 & -1 & 0 \\ -1 & 0 & 0\end{array}\right], B=\left[\begin{array}{ccc}0 & 1 & 0 \\ 1 & 0 & 0 \\ 0 & 0 & 1\end{array}\right]\)
then \(\left(\mathbf{A}^{-1} \mathbf{B}\right)^{-1}+\left(\mathbf{A} \mathbf{B}^{-1}\right)^{-1}=\)

1 \(\left[\begin{array}{ccc}1 & 0 & 0 \\ 0 & -2 & 0 \\ 0 & 0 & 2\end{array}\right]\)
2 \(\left[\begin{array}{ccc}0 & -2 & 0 \\ 0 & 0 & -2 \\ -2 & 0 & 0\end{array}\right]\)
3 \(\left[\begin{array}{ccc}-2 & 0 & 0 \\ 0 & 0 & -2 \\ 0 & -2 & 0\end{array}\right]\)
4 \(\left[\begin{array}{ccc}0 & 0 & -2 \\ -2 & 0 & 0 \\ 0 & -2 & 0\end{array}\right]\)
Matrix and Determinant

78917 The value of \(t\) such that the matrix
\(\left(\begin{array}{ccc}1 & 3 & 2 \\ 2 & 5 & t \\ 4 & 7-t & -6\end{array}\right)\) has no inverse, are

1 3,2
2 \(3,-2\)
3 \(-3,2\)
4 \(-3,-2\)
Matrix and Determinant

78918 If \(\left(\begin{array}{ccc}5 & a & -7 \\ b & -7 & c \\ -7 & d & -1\end{array}\right)\) is the adjoint of the matrix
\(\left(\begin{array}{lll}1 & 2 & 3 \\ 2 & 3 & 1 \\ 3 & 1 & 2\end{array}\right)\), then \(\mathbf{a}+\mathbf{b}+\mathbf{c}+\mathbf{d}=\)

1 8
2 10
3 0
4 2
Matrix and Determinant

78919 If \(A=\left[\begin{array}{ccc}1 & -2 & 2 \\ 2 & -6 & 5 \\ 5 & 0 & 4\end{array}\right]\) then Adj \(A=\)

1 \(\left[\begin{array}{ccc}-24 & 8 & 2 \\ 17 & -6 & -1 \\ 30 & -10 & 2\end{array}\right]\)
2 \(\left[\begin{array}{ccc}-24 & 8 & 2 \\ 17 & -6 & 1 \\ -30 & -10 & -2\end{array}\right]\)
3 \(\left[\begin{array}{ccc}-24 & 8 & 2 \\ 17 & -6 & -1 \\ 30 & -10 & -2\end{array}\right]\)
4 \(\left[\begin{array}{ccc}24 & -8 & 2 \\ -17 & -6 & 1 \\ 30 & -10 & -2\end{array}\right]\)
Matrix and Determinant

78920 Let \(A=\left[\begin{array}{ccc}0 & 0 & -1 \\ 0 & -1 & 0 \\ -1 & 0 & 0\end{array}\right], B=\left[\begin{array}{ccc}0 & 1 & 0 \\ 1 & 0 & 0 \\ 0 & 0 & 1\end{array}\right]\)
then \(\left(\mathbf{A}^{-1} \mathbf{B}\right)^{-1}+\left(\mathbf{A} \mathbf{B}^{-1}\right)^{-1}=\)

1 \(\left[\begin{array}{ccc}1 & 0 & 0 \\ 0 & -2 & 0 \\ 0 & 0 & 2\end{array}\right]\)
2 \(\left[\begin{array}{ccc}0 & -2 & 0 \\ 0 & 0 & -2 \\ -2 & 0 & 0\end{array}\right]\)
3 \(\left[\begin{array}{ccc}-2 & 0 & 0 \\ 0 & 0 & -2 \\ 0 & -2 & 0\end{array}\right]\)
4 \(\left[\begin{array}{ccc}0 & 0 & -2 \\ -2 & 0 & 0 \\ 0 & -2 & 0\end{array}\right]\)
Matrix and Determinant

78917 The value of \(t\) such that the matrix
\(\left(\begin{array}{ccc}1 & 3 & 2 \\ 2 & 5 & t \\ 4 & 7-t & -6\end{array}\right)\) has no inverse, are

1 3,2
2 \(3,-2\)
3 \(-3,2\)
4 \(-3,-2\)
Matrix and Determinant

78918 If \(\left(\begin{array}{ccc}5 & a & -7 \\ b & -7 & c \\ -7 & d & -1\end{array}\right)\) is the adjoint of the matrix
\(\left(\begin{array}{lll}1 & 2 & 3 \\ 2 & 3 & 1 \\ 3 & 1 & 2\end{array}\right)\), then \(\mathbf{a}+\mathbf{b}+\mathbf{c}+\mathbf{d}=\)

1 8
2 10
3 0
4 2
Matrix and Determinant

78919 If \(A=\left[\begin{array}{ccc}1 & -2 & 2 \\ 2 & -6 & 5 \\ 5 & 0 & 4\end{array}\right]\) then Adj \(A=\)

1 \(\left[\begin{array}{ccc}-24 & 8 & 2 \\ 17 & -6 & -1 \\ 30 & -10 & 2\end{array}\right]\)
2 \(\left[\begin{array}{ccc}-24 & 8 & 2 \\ 17 & -6 & 1 \\ -30 & -10 & -2\end{array}\right]\)
3 \(\left[\begin{array}{ccc}-24 & 8 & 2 \\ 17 & -6 & -1 \\ 30 & -10 & -2\end{array}\right]\)
4 \(\left[\begin{array}{ccc}24 & -8 & 2 \\ -17 & -6 & 1 \\ 30 & -10 & -2\end{array}\right]\)
Matrix and Determinant

78920 Let \(A=\left[\begin{array}{ccc}0 & 0 & -1 \\ 0 & -1 & 0 \\ -1 & 0 & 0\end{array}\right], B=\left[\begin{array}{ccc}0 & 1 & 0 \\ 1 & 0 & 0 \\ 0 & 0 & 1\end{array}\right]\)
then \(\left(\mathbf{A}^{-1} \mathbf{B}\right)^{-1}+\left(\mathbf{A} \mathbf{B}^{-1}\right)^{-1}=\)

1 \(\left[\begin{array}{ccc}1 & 0 & 0 \\ 0 & -2 & 0 \\ 0 & 0 & 2\end{array}\right]\)
2 \(\left[\begin{array}{ccc}0 & -2 & 0 \\ 0 & 0 & -2 \\ -2 & 0 & 0\end{array}\right]\)
3 \(\left[\begin{array}{ccc}-2 & 0 & 0 \\ 0 & 0 & -2 \\ 0 & -2 & 0\end{array}\right]\)
4 \(\left[\begin{array}{ccc}0 & 0 & -2 \\ -2 & 0 & 0 \\ 0 & -2 & 0\end{array}\right]\)
Matrix and Determinant

78917 The value of \(t\) such that the matrix
\(\left(\begin{array}{ccc}1 & 3 & 2 \\ 2 & 5 & t \\ 4 & 7-t & -6\end{array}\right)\) has no inverse, are

1 3,2
2 \(3,-2\)
3 \(-3,2\)
4 \(-3,-2\)
Matrix and Determinant

78918 If \(\left(\begin{array}{ccc}5 & a & -7 \\ b & -7 & c \\ -7 & d & -1\end{array}\right)\) is the adjoint of the matrix
\(\left(\begin{array}{lll}1 & 2 & 3 \\ 2 & 3 & 1 \\ 3 & 1 & 2\end{array}\right)\), then \(\mathbf{a}+\mathbf{b}+\mathbf{c}+\mathbf{d}=\)

1 8
2 10
3 0
4 2
Matrix and Determinant

78919 If \(A=\left[\begin{array}{ccc}1 & -2 & 2 \\ 2 & -6 & 5 \\ 5 & 0 & 4\end{array}\right]\) then Adj \(A=\)

1 \(\left[\begin{array}{ccc}-24 & 8 & 2 \\ 17 & -6 & -1 \\ 30 & -10 & 2\end{array}\right]\)
2 \(\left[\begin{array}{ccc}-24 & 8 & 2 \\ 17 & -6 & 1 \\ -30 & -10 & -2\end{array}\right]\)
3 \(\left[\begin{array}{ccc}-24 & 8 & 2 \\ 17 & -6 & -1 \\ 30 & -10 & -2\end{array}\right]\)
4 \(\left[\begin{array}{ccc}24 & -8 & 2 \\ -17 & -6 & 1 \\ 30 & -10 & -2\end{array}\right]\)
Matrix and Determinant

78920 Let \(A=\left[\begin{array}{ccc}0 & 0 & -1 \\ 0 & -1 & 0 \\ -1 & 0 & 0\end{array}\right], B=\left[\begin{array}{ccc}0 & 1 & 0 \\ 1 & 0 & 0 \\ 0 & 0 & 1\end{array}\right]\)
then \(\left(\mathbf{A}^{-1} \mathbf{B}\right)^{-1}+\left(\mathbf{A} \mathbf{B}^{-1}\right)^{-1}=\)

1 \(\left[\begin{array}{ccc}1 & 0 & 0 \\ 0 & -2 & 0 \\ 0 & 0 & 2\end{array}\right]\)
2 \(\left[\begin{array}{ccc}0 & -2 & 0 \\ 0 & 0 & -2 \\ -2 & 0 & 0\end{array}\right]\)
3 \(\left[\begin{array}{ccc}-2 & 0 & 0 \\ 0 & 0 & -2 \\ 0 & -2 & 0\end{array}\right]\)
4 \(\left[\begin{array}{ccc}0 & 0 & -2 \\ -2 & 0 & 0 \\ 0 & -2 & 0\end{array}\right]\)