Solution of System of Linear Equation Using Matrix
Matrix and Determinant

78980 If matrix \(A=\left|\begin{array}{ccc}1 & 0 & -1 \\ 3 & 4 & 5 \\ 0 & 6 & 7\end{array}\right|\) and its inverse is denoted by \(A^{-1}=\left|\begin{array}{lll}a_{11} & a_{12} & a_{13} \\ a_{21} & a_{22} & a_{23} \\ a_{31} & a_{32} & a_{33}\end{array}\right|\), then the value of \(a_{23}\) is

1 \(\frac{21}{20}\)
2 \(\frac{1}{5}\)
3 \(-\frac{2}{5}\)
4 \(\frac{2}{5}\)
Matrix and Determinant

78981 If \(A=\left[\begin{array}{ll}4 & 2 \\ 3 & 4\end{array}\right],|\operatorname{adj} A|\) is equal to:

1 6
2 16
3 10
4 none of these
Matrix and Determinant

78982 Inverse matrix of \(\left[\begin{array}{ll}4 & 7 \\ 1 & 2\end{array}\right]\) is equal to :

1 \(\left[\begin{array}{cc}2 & -7 \\ -1 & 4\end{array}\right]\)
2 \(\left[\begin{array}{cc}2 & -1 \\ -7 & 4\end{array}\right]\)
3 \(\left[\begin{array}{cc}-2 & 7 \\ 1 & -4\end{array}\right]\)
4 \(\left[\begin{array}{cc}-2 & 1 \\ 7 & -4\end{array}\right]\)
Matrix and Determinant

78983 If \(\mathbf{A}^{\mathbf{3}}=\mathbf{0}\), then \(\mathrm{I}+\mathrm{A}+\mathrm{A}^{2}\) equals

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

78980 If matrix \(A=\left|\begin{array}{ccc}1 & 0 & -1 \\ 3 & 4 & 5 \\ 0 & 6 & 7\end{array}\right|\) and its inverse is denoted by \(A^{-1}=\left|\begin{array}{lll}a_{11} & a_{12} & a_{13} \\ a_{21} & a_{22} & a_{23} \\ a_{31} & a_{32} & a_{33}\end{array}\right|\), then the value of \(a_{23}\) is

1 \(\frac{21}{20}\)
2 \(\frac{1}{5}\)
3 \(-\frac{2}{5}\)
4 \(\frac{2}{5}\)
Matrix and Determinant

78981 If \(A=\left[\begin{array}{ll}4 & 2 \\ 3 & 4\end{array}\right],|\operatorname{adj} A|\) is equal to:

1 6
2 16
3 10
4 none of these
Matrix and Determinant

78982 Inverse matrix of \(\left[\begin{array}{ll}4 & 7 \\ 1 & 2\end{array}\right]\) is equal to :

1 \(\left[\begin{array}{cc}2 & -7 \\ -1 & 4\end{array}\right]\)
2 \(\left[\begin{array}{cc}2 & -1 \\ -7 & 4\end{array}\right]\)
3 \(\left[\begin{array}{cc}-2 & 7 \\ 1 & -4\end{array}\right]\)
4 \(\left[\begin{array}{cc}-2 & 1 \\ 7 & -4\end{array}\right]\)
Matrix and Determinant

78983 If \(\mathbf{A}^{\mathbf{3}}=\mathbf{0}\), then \(\mathrm{I}+\mathrm{A}+\mathrm{A}^{2}\) equals

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

78980 If matrix \(A=\left|\begin{array}{ccc}1 & 0 & -1 \\ 3 & 4 & 5 \\ 0 & 6 & 7\end{array}\right|\) and its inverse is denoted by \(A^{-1}=\left|\begin{array}{lll}a_{11} & a_{12} & a_{13} \\ a_{21} & a_{22} & a_{23} \\ a_{31} & a_{32} & a_{33}\end{array}\right|\), then the value of \(a_{23}\) is

1 \(\frac{21}{20}\)
2 \(\frac{1}{5}\)
3 \(-\frac{2}{5}\)
4 \(\frac{2}{5}\)
Matrix and Determinant

78981 If \(A=\left[\begin{array}{ll}4 & 2 \\ 3 & 4\end{array}\right],|\operatorname{adj} A|\) is equal to:

1 6
2 16
3 10
4 none of these
Matrix and Determinant

78982 Inverse matrix of \(\left[\begin{array}{ll}4 & 7 \\ 1 & 2\end{array}\right]\) is equal to :

1 \(\left[\begin{array}{cc}2 & -7 \\ -1 & 4\end{array}\right]\)
2 \(\left[\begin{array}{cc}2 & -1 \\ -7 & 4\end{array}\right]\)
3 \(\left[\begin{array}{cc}-2 & 7 \\ 1 & -4\end{array}\right]\)
4 \(\left[\begin{array}{cc}-2 & 1 \\ 7 & -4\end{array}\right]\)
Matrix and Determinant

78983 If \(\mathbf{A}^{\mathbf{3}}=\mathbf{0}\), then \(\mathrm{I}+\mathrm{A}+\mathrm{A}^{2}\) equals

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

78980 If matrix \(A=\left|\begin{array}{ccc}1 & 0 & -1 \\ 3 & 4 & 5 \\ 0 & 6 & 7\end{array}\right|\) and its inverse is denoted by \(A^{-1}=\left|\begin{array}{lll}a_{11} & a_{12} & a_{13} \\ a_{21} & a_{22} & a_{23} \\ a_{31} & a_{32} & a_{33}\end{array}\right|\), then the value of \(a_{23}\) is

1 \(\frac{21}{20}\)
2 \(\frac{1}{5}\)
3 \(-\frac{2}{5}\)
4 \(\frac{2}{5}\)
Matrix and Determinant

78981 If \(A=\left[\begin{array}{ll}4 & 2 \\ 3 & 4\end{array}\right],|\operatorname{adj} A|\) is equal to:

1 6
2 16
3 10
4 none of these
Matrix and Determinant

78982 Inverse matrix of \(\left[\begin{array}{ll}4 & 7 \\ 1 & 2\end{array}\right]\) is equal to :

1 \(\left[\begin{array}{cc}2 & -7 \\ -1 & 4\end{array}\right]\)
2 \(\left[\begin{array}{cc}2 & -1 \\ -7 & 4\end{array}\right]\)
3 \(\left[\begin{array}{cc}-2 & 7 \\ 1 & -4\end{array}\right]\)
4 \(\left[\begin{array}{cc}-2 & 1 \\ 7 & -4\end{array}\right]\)
Matrix and Determinant

78983 If \(\mathbf{A}^{\mathbf{3}}=\mathbf{0}\), then \(\mathrm{I}+\mathrm{A}+\mathrm{A}^{2}\) equals

1 \(\mathrm{I}-\mathrm{A}\)
2 \((\mathrm{I}-\mathrm{A})^{-1}\)
3 \((\mathrm{I}+\mathrm{A})^{-1}\)
4 \(\mathrm{A}\)
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