79058 If \(\left|\begin{array}{ccc}p & q-y & r-z \\ p-x & q & r-z\end{array}\right|=0\), then the value of \(\mathbf{p}-\mathbf{x} \quad \mathbf{q}-\mathbf{y} \quad \mathbf{r}\)
\(\frac{\mathbf{p}}{\mathbf{x}}+\frac{\mathbf{q}}{\mathbf{y}}+\frac{\mathbf{r}}{\mathbf{z}}\) is

79059 Let \(M=\left(\begin{array}{lll}0 & 0 & 1 \\ 0 & 1 & 0 \\ 1 & 0 & 0\end{array}\right)\). Then \(\frac{1}{3} \operatorname{det}\left(3\left(M+M^{T}\right)\right)\) is

79061 What is the value of the determinant?
\(\left|\begin{array}{ccc} 2 & 3 & -2 \\ 1 & 2 & 3 \\ -2 & 1 & -3 \end{array}\right|\)

79062 If \(\omega\) is a root of the equation \(x+\frac{1}{x}+1=0\), then
\(\left|\begin{array}{ccc} 1 & 1+\omega & 1+\omega+\omega^{2} \\ 3 & 4+3 \omega & 5+4 \omega+3 \omega^{2} \\ 6 & 9+6 \omega & 11+9 \omega+6 \omega^{2} \end{array}\right|=\)

79058 If \(\left|\begin{array}{ccc}p & q-y & r-z \\ p-x & q & r-z\end{array}\right|=0\), then the value of \(\mathbf{p}-\mathbf{x} \quad \mathbf{q}-\mathbf{y} \quad \mathbf{r}\)
\(\frac{\mathbf{p}}{\mathbf{x}}+\frac{\mathbf{q}}{\mathbf{y}}+\frac{\mathbf{r}}{\mathbf{z}}\) is

79059 Let \(M=\left(\begin{array}{lll}0 & 0 & 1 \\ 0 & 1 & 0 \\ 1 & 0 & 0\end{array}\right)\). Then \(\frac{1}{3} \operatorname{det}\left(3\left(M+M^{T}\right)\right)\) is

79061 What is the value of the determinant?
\(\left|\begin{array}{ccc} 2 & 3 & -2 \\ 1 & 2 & 3 \\ -2 & 1 & -3 \end{array}\right|\)

79062 If \(\omega\) is a root of the equation \(x+\frac{1}{x}+1=0\), then
\(\left|\begin{array}{ccc} 1 & 1+\omega & 1+\omega+\omega^{2} \\ 3 & 4+3 \omega & 5+4 \omega+3 \omega^{2} \\ 6 & 9+6 \omega & 11+9 \omega+6 \omega^{2} \end{array}\right|=\)

79058 If \(\left|\begin{array}{ccc}p & q-y & r-z \\ p-x & q & r-z\end{array}\right|=0\), then the value of \(\mathbf{p}-\mathbf{x} \quad \mathbf{q}-\mathbf{y} \quad \mathbf{r}\)
\(\frac{\mathbf{p}}{\mathbf{x}}+\frac{\mathbf{q}}{\mathbf{y}}+\frac{\mathbf{r}}{\mathbf{z}}\) is

79059 Let \(M=\left(\begin{array}{lll}0 & 0 & 1 \\ 0 & 1 & 0 \\ 1 & 0 & 0\end{array}\right)\). Then \(\frac{1}{3} \operatorname{det}\left(3\left(M+M^{T}\right)\right)\) is

79061 What is the value of the determinant?
\(\left|\begin{array}{ccc} 2 & 3 & -2 \\ 1 & 2 & 3 \\ -2 & 1 & -3 \end{array}\right|\)

79062 If \(\omega\) is a root of the equation \(x+\frac{1}{x}+1=0\), then
\(\left|\begin{array}{ccc} 1 & 1+\omega & 1+\omega+\omega^{2} \\ 3 & 4+3 \omega & 5+4 \omega+3 \omega^{2} \\ 6 & 9+6 \omega & 11+9 \omega+6 \omega^{2} \end{array}\right|=\)

79058 If \(\left|\begin{array}{ccc}p & q-y & r-z \\ p-x & q & r-z\end{array}\right|=0\), then the value of \(\mathbf{p}-\mathbf{x} \quad \mathbf{q}-\mathbf{y} \quad \mathbf{r}\)
\(\frac{\mathbf{p}}{\mathbf{x}}+\frac{\mathbf{q}}{\mathbf{y}}+\frac{\mathbf{r}}{\mathbf{z}}\) is

79059 Let \(M=\left(\begin{array}{lll}0 & 0 & 1 \\ 0 & 1 & 0 \\ 1 & 0 & 0\end{array}\right)\). Then \(\frac{1}{3} \operatorname{det}\left(3\left(M+M^{T}\right)\right)\) is

79061 What is the value of the determinant?
\(\left|\begin{array}{ccc} 2 & 3 & -2 \\ 1 & 2 & 3 \\ -2 & 1 & -3 \end{array}\right|\)

79062 If \(\omega\) is a root of the equation \(x+\frac{1}{x}+1=0\), then
\(\left|\begin{array}{ccc} 1 & 1+\omega & 1+\omega+\omega^{2} \\ 3 & 4+3 \omega & 5+4 \omega+3 \omega^{2} \\ 6 & 9+6 \omega & 11+9 \omega+6 \omega^{2} \end{array}\right|=\)