79052 If \(p=\left[\begin{array}{lll}1 & \alpha & 3 \\ 1 & 3 & 3 \\ 2 & 4 & 4\end{array}\right]\), is the adjoint of \(3 \times 3\) matrix
\(A\) and \(\operatorname{det} A=4\), then \(\alpha\) is equal to

79053 Let \(a, b, c\) be such that \(b+c \neq 0\) and
\(\left|\begin{array}{ccc} \mathbf{a} & \mathbf{a}+\mathbf{1} & \mathbf{a}-\mathbf{1} \\ -\mathbf{b} & \mathbf{b}+\mathbf{1} & \mathbf{b}-\mathbf{1} \\ \mathbf{c} & \mathbf{c}-\mathbf{1} & \mathbf{c}+\mathbf{1} \end{array}\right|\)\(+\left|\begin{array}{ccc} \mathbf{a}+\mathbf{1} & \mathbf{b}+\mathbf{1} & \mathbf{c}-\mathbf{1} \\ \mathbf{a - 1} & \mathbf{b}-\mathbf{1} & \mathbf{c}+\mathbf{1} \\ (-\mathbf{1})^{\mathrm{n}+2} \mathbf{a} & (-\mathbf{- 1})^{\mathrm{n}-1} \mathbf{b} & (-\mathbf{1})^{\mathrm{n}} \mathbf{c} \end{array}\right|=\mathbf{0},\)
then the value of ' \(n\) ' is

79055 \(\left|\begin{array}{cccc} \mathbf{a} & \mathbf{b} & \mathbf{c} & \mathbf{d} \\ -\mathbf{a} & \mathbf{b} & \mathbf{c} & \mathbf{d} \\ -\mathbf{a} & -\mathbf{b} & \mathbf{c} & \mathbf{d} \\ -\mathbf{a} & -\mathbf{b} & -\mathbf{c} & \mathbf{d} \end{array}\right|=\)

79057 If the value of a third order determinant is 16 , then the value of the determinant formed by replacing each of its elements by its cofactor is

79052 If \(p=\left[\begin{array}{lll}1 & \alpha & 3 \\ 1 & 3 & 3 \\ 2 & 4 & 4\end{array}\right]\), is the adjoint of \(3 \times 3\) matrix
\(A\) and \(\operatorname{det} A=4\), then \(\alpha\) is equal to

79053 Let \(a, b, c\) be such that \(b+c \neq 0\) and
\(\left|\begin{array}{ccc} \mathbf{a} & \mathbf{a}+\mathbf{1} & \mathbf{a}-\mathbf{1} \\ -\mathbf{b} & \mathbf{b}+\mathbf{1} & \mathbf{b}-\mathbf{1} \\ \mathbf{c} & \mathbf{c}-\mathbf{1} & \mathbf{c}+\mathbf{1} \end{array}\right|\)\(+\left|\begin{array}{ccc} \mathbf{a}+\mathbf{1} & \mathbf{b}+\mathbf{1} & \mathbf{c}-\mathbf{1} \\ \mathbf{a - 1} & \mathbf{b}-\mathbf{1} & \mathbf{c}+\mathbf{1} \\ (-\mathbf{1})^{\mathrm{n}+2} \mathbf{a} & (-\mathbf{- 1})^{\mathrm{n}-1} \mathbf{b} & (-\mathbf{1})^{\mathrm{n}} \mathbf{c} \end{array}\right|=\mathbf{0},\)
then the value of ' \(n\) ' is

79055 \(\left|\begin{array}{cccc} \mathbf{a} & \mathbf{b} & \mathbf{c} & \mathbf{d} \\ -\mathbf{a} & \mathbf{b} & \mathbf{c} & \mathbf{d} \\ -\mathbf{a} & -\mathbf{b} & \mathbf{c} & \mathbf{d} \\ -\mathbf{a} & -\mathbf{b} & -\mathbf{c} & \mathbf{d} \end{array}\right|=\)

79057 If the value of a third order determinant is 16 , then the value of the determinant formed by replacing each of its elements by its cofactor is

79052 If \(p=\left[\begin{array}{lll}1 & \alpha & 3 \\ 1 & 3 & 3 \\ 2 & 4 & 4\end{array}\right]\), is the adjoint of \(3 \times 3\) matrix
\(A\) and \(\operatorname{det} A=4\), then \(\alpha\) is equal to

79053 Let \(a, b, c\) be such that \(b+c \neq 0\) and
\(\left|\begin{array}{ccc} \mathbf{a} & \mathbf{a}+\mathbf{1} & \mathbf{a}-\mathbf{1} \\ -\mathbf{b} & \mathbf{b}+\mathbf{1} & \mathbf{b}-\mathbf{1} \\ \mathbf{c} & \mathbf{c}-\mathbf{1} & \mathbf{c}+\mathbf{1} \end{array}\right|\)\(+\left|\begin{array}{ccc} \mathbf{a}+\mathbf{1} & \mathbf{b}+\mathbf{1} & \mathbf{c}-\mathbf{1} \\ \mathbf{a - 1} & \mathbf{b}-\mathbf{1} & \mathbf{c}+\mathbf{1} \\ (-\mathbf{1})^{\mathrm{n}+2} \mathbf{a} & (-\mathbf{- 1})^{\mathrm{n}-1} \mathbf{b} & (-\mathbf{1})^{\mathrm{n}} \mathbf{c} \end{array}\right|=\mathbf{0},\)
then the value of ' \(n\) ' is

79055 \(\left|\begin{array}{cccc} \mathbf{a} & \mathbf{b} & \mathbf{c} & \mathbf{d} \\ -\mathbf{a} & \mathbf{b} & \mathbf{c} & \mathbf{d} \\ -\mathbf{a} & -\mathbf{b} & \mathbf{c} & \mathbf{d} \\ -\mathbf{a} & -\mathbf{b} & -\mathbf{c} & \mathbf{d} \end{array}\right|=\)

79057 If the value of a third order determinant is 16 , then the value of the determinant formed by replacing each of its elements by its cofactor is

79052 If \(p=\left[\begin{array}{lll}1 & \alpha & 3 \\ 1 & 3 & 3 \\ 2 & 4 & 4\end{array}\right]\), is the adjoint of \(3 \times 3\) matrix
\(A\) and \(\operatorname{det} A=4\), then \(\alpha\) is equal to

79053 Let \(a, b, c\) be such that \(b+c \neq 0\) and
\(\left|\begin{array}{ccc} \mathbf{a} & \mathbf{a}+\mathbf{1} & \mathbf{a}-\mathbf{1} \\ -\mathbf{b} & \mathbf{b}+\mathbf{1} & \mathbf{b}-\mathbf{1} \\ \mathbf{c} & \mathbf{c}-\mathbf{1} & \mathbf{c}+\mathbf{1} \end{array}\right|\)\(+\left|\begin{array}{ccc} \mathbf{a}+\mathbf{1} & \mathbf{b}+\mathbf{1} & \mathbf{c}-\mathbf{1} \\ \mathbf{a - 1} & \mathbf{b}-\mathbf{1} & \mathbf{c}+\mathbf{1} \\ (-\mathbf{1})^{\mathrm{n}+2} \mathbf{a} & (-\mathbf{- 1})^{\mathrm{n}-1} \mathbf{b} & (-\mathbf{1})^{\mathrm{n}} \mathbf{c} \end{array}\right|=\mathbf{0},\)
then the value of ' \(n\) ' is

79055 \(\left|\begin{array}{cccc} \mathbf{a} & \mathbf{b} & \mathbf{c} & \mathbf{d} \\ -\mathbf{a} & \mathbf{b} & \mathbf{c} & \mathbf{d} \\ -\mathbf{a} & -\mathbf{b} & \mathbf{c} & \mathbf{d} \\ -\mathbf{a} & -\mathbf{b} & -\mathbf{c} & \mathbf{d} \end{array}\right|=\)

79057 If the value of a third order determinant is 16 , then the value of the determinant formed by replacing each of its elements by its cofactor is