78900 If the matrices \(A=\left[\begin{array}{ccc}1 & 1 & 2 \\ 1 & 3 & 4 \\ 1 & -1 & 3\end{array}\right], B=\operatorname{adj} A\) and \(C=3 A\), then \(\frac{|\operatorname{adj} \mathbf{B}|}{|\mathbf{C}|}\) is equal to

78901 If \(P=\left[\begin{array}{lll}1 & \alpha & 3 \\ 1 & 3 & 3 \\ 2 & 4 & 4\end{array}\right]\) is the adjoint of a \(3 \times 3\) matrix
\(A\) and \(|A|=4\), then \(\alpha\) is equal to

78902 If \(A=\left(\begin{array}{ll}2 & 2 \\ 9 & 4\end{array}\right)\) and \(I=\left(\begin{array}{ll}1 & 0 \\ 0 & 1\end{array}\right)\), then \(10 A^{-1}\) is equal to

78903 If \(\left[\begin{array}{ll}1 & 1 \\ 0 & 1\end{array}\right] \cdot\left[\begin{array}{ll}1 & 2 \\ 0 & 1\end{array}\right] \cdot\left[\begin{array}{ll}1 & 3 \\ 0 & 1\end{array}\right] \cdots \cdot \cdot\left[\begin{array}{cc}1 & n-1 \\ 0 & 1\end{array}\right]=\)
\(\left[\begin{array}{cc} 1 & 78 \\ 0 & 1 \end{array}\right] \text {, then the inverse of }\left[\begin{array}{ll}
1 & n \\ 0 & 1 \end{array}\right] \text { is }\)

78900 If the matrices \(A=\left[\begin{array}{ccc}1 & 1 & 2 \\ 1 & 3 & 4 \\ 1 & -1 & 3\end{array}\right], B=\operatorname{adj} A\) and \(C=3 A\), then \(\frac{|\operatorname{adj} \mathbf{B}|}{|\mathbf{C}|}\) is equal to

78901 If \(P=\left[\begin{array}{lll}1 & \alpha & 3 \\ 1 & 3 & 3 \\ 2 & 4 & 4\end{array}\right]\) is the adjoint of a \(3 \times 3\) matrix
\(A\) and \(|A|=4\), then \(\alpha\) is equal to

78902 If \(A=\left(\begin{array}{ll}2 & 2 \\ 9 & 4\end{array}\right)\) and \(I=\left(\begin{array}{ll}1 & 0 \\ 0 & 1\end{array}\right)\), then \(10 A^{-1}\) is equal to

78903 If \(\left[\begin{array}{ll}1 & 1 \\ 0 & 1\end{array}\right] \cdot\left[\begin{array}{ll}1 & 2 \\ 0 & 1\end{array}\right] \cdot\left[\begin{array}{ll}1 & 3 \\ 0 & 1\end{array}\right] \cdots \cdot \cdot\left[\begin{array}{cc}1 & n-1 \\ 0 & 1\end{array}\right]=\)
\(\left[\begin{array}{cc} 1 & 78 \\ 0 & 1 \end{array}\right] \text {, then the inverse of }\left[\begin{array}{ll}
1 & n \\ 0 & 1 \end{array}\right] \text { is }\)

78900 If the matrices \(A=\left[\begin{array}{ccc}1 & 1 & 2 \\ 1 & 3 & 4 \\ 1 & -1 & 3\end{array}\right], B=\operatorname{adj} A\) and \(C=3 A\), then \(\frac{|\operatorname{adj} \mathbf{B}|}{|\mathbf{C}|}\) is equal to

78901 If \(P=\left[\begin{array}{lll}1 & \alpha & 3 \\ 1 & 3 & 3 \\ 2 & 4 & 4\end{array}\right]\) is the adjoint of a \(3 \times 3\) matrix
\(A\) and \(|A|=4\), then \(\alpha\) is equal to

78902 If \(A=\left(\begin{array}{ll}2 & 2 \\ 9 & 4\end{array}\right)\) and \(I=\left(\begin{array}{ll}1 & 0 \\ 0 & 1\end{array}\right)\), then \(10 A^{-1}\) is equal to

78903 If \(\left[\begin{array}{ll}1 & 1 \\ 0 & 1\end{array}\right] \cdot\left[\begin{array}{ll}1 & 2 \\ 0 & 1\end{array}\right] \cdot\left[\begin{array}{ll}1 & 3 \\ 0 & 1\end{array}\right] \cdots \cdot \cdot\left[\begin{array}{cc}1 & n-1 \\ 0 & 1\end{array}\right]=\)
\(\left[\begin{array}{cc} 1 & 78 \\ 0 & 1 \end{array}\right] \text {, then the inverse of }\left[\begin{array}{ll}
1 & n \\ 0 & 1 \end{array}\right] \text { is }\)

78900 If the matrices \(A=\left[\begin{array}{ccc}1 & 1 & 2 \\ 1 & 3 & 4 \\ 1 & -1 & 3\end{array}\right], B=\operatorname{adj} A\) and \(C=3 A\), then \(\frac{|\operatorname{adj} \mathbf{B}|}{|\mathbf{C}|}\) is equal to

78901 If \(P=\left[\begin{array}{lll}1 & \alpha & 3 \\ 1 & 3 & 3 \\ 2 & 4 & 4\end{array}\right]\) is the adjoint of a \(3 \times 3\) matrix
\(A\) and \(|A|=4\), then \(\alpha\) is equal to

78902 If \(A=\left(\begin{array}{ll}2 & 2 \\ 9 & 4\end{array}\right)\) and \(I=\left(\begin{array}{ll}1 & 0 \\ 0 & 1\end{array}\right)\), then \(10 A^{-1}\) is equal to

78903 If \(\left[\begin{array}{ll}1 & 1 \\ 0 & 1\end{array}\right] \cdot\left[\begin{array}{ll}1 & 2 \\ 0 & 1\end{array}\right] \cdot\left[\begin{array}{ll}1 & 3 \\ 0 & 1\end{array}\right] \cdots \cdot \cdot\left[\begin{array}{cc}1 & n-1 \\ 0 & 1\end{array}\right]=\)
\(\left[\begin{array}{cc} 1 & 78 \\ 0 & 1 \end{array}\right] \text {, then the inverse of }\left[\begin{array}{ll}
1 & n \\ 0 & 1 \end{array}\right] \text { is }\)