79194 Let \(A=\left(\begin{array}{ccc}3-t & 1 & 0 \\ -1 & 3-t & 1 \\ 0 & -1 & 0\end{array}\right)\) and \(\operatorname{det} A=5\), then

79195 The determinant
\(\left|\begin{array}{ccc}a^{2}+10 & \mathbf{a b} & \mathbf{a c} \\ \mathbf{a b} & \mathbf{b}^{2}+\mathbf{1 0} & \mathbf{b c} \\ \mathbf{a c} & \mathbf{b c} & \mathbf{c}^{2}+\mathbf{1 0}\end{array}\right|\) is

79196 Let \(A=\left(\begin{array}{ccc}1 & 0 & 0 \\ 0 & \text { cost } & \text { sint } \\ 0 & - \text { sint } & \text { cost }\end{array}\right)\)
Let \(\lambda_{1}, \lambda_{2}, \lambda_{3}\) be the \(\operatorname{roots}\) of \(\operatorname{det}\left(\mathbf{A}-\lambda \mathbf{I}_{3}\right)=\mathbf{0}\), where \(\mathbf{I}_{3}\) denotes the identity matrix. If \(\lambda_{1}+\lambda_{2}+\lambda_{3}=\sqrt{2}+1\) then the set of possible values of \(t,-\pi \leq t<\pi\) is

79197 If \(\Delta(x)=\left|\begin{array}{ccc}x-2 & (x-1)^{2} & x^{3} \\ x-1 & x^{2} & (x+1)^{3} \\ x & (x+1)^{2} & (x+2)^{3}\end{array}\right|, \quad\) then

79198 If \(\alpha, \beta, \gamma\) are the roots of \(x^{3}+a^{2} x+b=0\), then the value of \(\left|\begin{array}{lll}\alpha & \boldsymbol{\beta} & \gamma \\ \boldsymbol{\beta} & \gamma & \alpha \\ \gamma & \alpha & \beta\end{array}\right|\) is

79194 Let \(A=\left(\begin{array}{ccc}3-t & 1 & 0 \\ -1 & 3-t & 1 \\ 0 & -1 & 0\end{array}\right)\) and \(\operatorname{det} A=5\), then

79195 The determinant
\(\left|\begin{array}{ccc}a^{2}+10 & \mathbf{a b} & \mathbf{a c} \\ \mathbf{a b} & \mathbf{b}^{2}+\mathbf{1 0} & \mathbf{b c} \\ \mathbf{a c} & \mathbf{b c} & \mathbf{c}^{2}+\mathbf{1 0}\end{array}\right|\) is

79196 Let \(A=\left(\begin{array}{ccc}1 & 0 & 0 \\ 0 & \text { cost } & \text { sint } \\ 0 & - \text { sint } & \text { cost }\end{array}\right)\)
Let \(\lambda_{1}, \lambda_{2}, \lambda_{3}\) be the \(\operatorname{roots}\) of \(\operatorname{det}\left(\mathbf{A}-\lambda \mathbf{I}_{3}\right)=\mathbf{0}\), where \(\mathbf{I}_{3}\) denotes the identity matrix. If \(\lambda_{1}+\lambda_{2}+\lambda_{3}=\sqrt{2}+1\) then the set of possible values of \(t,-\pi \leq t<\pi\) is

79197 If \(\Delta(x)=\left|\begin{array}{ccc}x-2 & (x-1)^{2} & x^{3} \\ x-1 & x^{2} & (x+1)^{3} \\ x & (x+1)^{2} & (x+2)^{3}\end{array}\right|, \quad\) then

79198 If \(\alpha, \beta, \gamma\) are the roots of \(x^{3}+a^{2} x+b=0\), then the value of \(\left|\begin{array}{lll}\alpha & \boldsymbol{\beta} & \gamma \\ \boldsymbol{\beta} & \gamma & \alpha \\ \gamma & \alpha & \beta\end{array}\right|\) is

79194 Let \(A=\left(\begin{array}{ccc}3-t & 1 & 0 \\ -1 & 3-t & 1 \\ 0 & -1 & 0\end{array}\right)\) and \(\operatorname{det} A=5\), then

79195 The determinant
\(\left|\begin{array}{ccc}a^{2}+10 & \mathbf{a b} & \mathbf{a c} \\ \mathbf{a b} & \mathbf{b}^{2}+\mathbf{1 0} & \mathbf{b c} \\ \mathbf{a c} & \mathbf{b c} & \mathbf{c}^{2}+\mathbf{1 0}\end{array}\right|\) is

79196 Let \(A=\left(\begin{array}{ccc}1 & 0 & 0 \\ 0 & \text { cost } & \text { sint } \\ 0 & - \text { sint } & \text { cost }\end{array}\right)\)
Let \(\lambda_{1}, \lambda_{2}, \lambda_{3}\) be the \(\operatorname{roots}\) of \(\operatorname{det}\left(\mathbf{A}-\lambda \mathbf{I}_{3}\right)=\mathbf{0}\), where \(\mathbf{I}_{3}\) denotes the identity matrix. If \(\lambda_{1}+\lambda_{2}+\lambda_{3}=\sqrt{2}+1\) then the set of possible values of \(t,-\pi \leq t<\pi\) is

79197 If \(\Delta(x)=\left|\begin{array}{ccc}x-2 & (x-1)^{2} & x^{3} \\ x-1 & x^{2} & (x+1)^{3} \\ x & (x+1)^{2} & (x+2)^{3}\end{array}\right|, \quad\) then

79198 If \(\alpha, \beta, \gamma\) are the roots of \(x^{3}+a^{2} x+b=0\), then the value of \(\left|\begin{array}{lll}\alpha & \boldsymbol{\beta} & \gamma \\ \boldsymbol{\beta} & \gamma & \alpha \\ \gamma & \alpha & \beta\end{array}\right|\) is

79194 Let \(A=\left(\begin{array}{ccc}3-t & 1 & 0 \\ -1 & 3-t & 1 \\ 0 & -1 & 0\end{array}\right)\) and \(\operatorname{det} A=5\), then

79195 The determinant
\(\left|\begin{array}{ccc}a^{2}+10 & \mathbf{a b} & \mathbf{a c} \\ \mathbf{a b} & \mathbf{b}^{2}+\mathbf{1 0} & \mathbf{b c} \\ \mathbf{a c} & \mathbf{b c} & \mathbf{c}^{2}+\mathbf{1 0}\end{array}\right|\) is

79196 Let \(A=\left(\begin{array}{ccc}1 & 0 & 0 \\ 0 & \text { cost } & \text { sint } \\ 0 & - \text { sint } & \text { cost }\end{array}\right)\)
Let \(\lambda_{1}, \lambda_{2}, \lambda_{3}\) be the \(\operatorname{roots}\) of \(\operatorname{det}\left(\mathbf{A}-\lambda \mathbf{I}_{3}\right)=\mathbf{0}\), where \(\mathbf{I}_{3}\) denotes the identity matrix. If \(\lambda_{1}+\lambda_{2}+\lambda_{3}=\sqrt{2}+1\) then the set of possible values of \(t,-\pi \leq t<\pi\) is

79197 If \(\Delta(x)=\left|\begin{array}{ccc}x-2 & (x-1)^{2} & x^{3} \\ x-1 & x^{2} & (x+1)^{3} \\ x & (x+1)^{2} & (x+2)^{3}\end{array}\right|, \quad\) then

79198 If \(\alpha, \beta, \gamma\) are the roots of \(x^{3}+a^{2} x+b=0\), then the value of \(\left|\begin{array}{lll}\alpha & \boldsymbol{\beta} & \gamma \\ \boldsymbol{\beta} & \gamma & \alpha \\ \gamma & \alpha & \beta\end{array}\right|\) is

79194 Let \(A=\left(\begin{array}{ccc}3-t & 1 & 0 \\ -1 & 3-t & 1 \\ 0 & -1 & 0\end{array}\right)\) and \(\operatorname{det} A=5\), then

79195 The determinant
\(\left|\begin{array}{ccc}a^{2}+10 & \mathbf{a b} & \mathbf{a c} \\ \mathbf{a b} & \mathbf{b}^{2}+\mathbf{1 0} & \mathbf{b c} \\ \mathbf{a c} & \mathbf{b c} & \mathbf{c}^{2}+\mathbf{1 0}\end{array}\right|\) is

79196 Let \(A=\left(\begin{array}{ccc}1 & 0 & 0 \\ 0 & \text { cost } & \text { sint } \\ 0 & - \text { sint } & \text { cost }\end{array}\right)\)
Let \(\lambda_{1}, \lambda_{2}, \lambda_{3}\) be the \(\operatorname{roots}\) of \(\operatorname{det}\left(\mathbf{A}-\lambda \mathbf{I}_{3}\right)=\mathbf{0}\), where \(\mathbf{I}_{3}\) denotes the identity matrix. If \(\lambda_{1}+\lambda_{2}+\lambda_{3}=\sqrt{2}+1\) then the set of possible values of \(t,-\pi \leq t<\pi\) is

79197 If \(\Delta(x)=\left|\begin{array}{ccc}x-2 & (x-1)^{2} & x^{3} \\ x-1 & x^{2} & (x+1)^{3} \\ x & (x+1)^{2} & (x+2)^{3}\end{array}\right|, \quad\) then

79198 If \(\alpha, \beta, \gamma\) are the roots of \(x^{3}+a^{2} x+b=0\), then the value of \(\left|\begin{array}{lll}\alpha & \boldsymbol{\beta} & \gamma \\ \boldsymbol{\beta} & \gamma & \alpha \\ \gamma & \alpha & \beta\end{array}\right|\) is