79020 If \(\mathbf{a}^{2}+b^{2}+c^{2}=-2\)
and \(f(x)=\left|\begin{array}{ccc}1+a^{2} x & \left(1+b^{2}\right) x & \left(1+c^{2}\right) x \\ \left(1+a^{2}\right) x & 1+b^{2} x & \left(1+c^{2}\right) x \\ \left(1+a^{2}\right) x & \left(1+b^{2}\right) x & 1+c^{2} x\end{array}\right|\)
then \(f(x)\) is a polynomial of degree

79021 Matrix \(M_{r}\) is defined as \(M_{r}=\left[\begin{array}{cc}r & r-1 \\ r-1 & r\end{array}\right]\) \(r \in N\) Value of \(\operatorname{det}\left(M_{1}\right)+\operatorname{det}\left(M_{2}\right)+\operatorname{det}\left(M_{3}\right)+\) ... + det \(\left(\mathbf{M}_{2007}\right)\) is

79022 If \(y y^{2} 1+y^{3}=0\) then
\(\left|\begin{array}{lll}z & z^{2} & 1+z^{3}\end{array}\right|\)

79023 If \(\cos 2 \theta=0\), then
\(\left|\begin{array}{ccc}0 & \cos \theta & \sin \theta \\ \cos \theta & \sin \theta & 0 \\ \sin \theta & 0 & \cos \theta\end{array}\right|^{2}=\)

79020 If \(\mathbf{a}^{2}+b^{2}+c^{2}=-2\)
and \(f(x)=\left|\begin{array}{ccc}1+a^{2} x & \left(1+b^{2}\right) x & \left(1+c^{2}\right) x \\ \left(1+a^{2}\right) x & 1+b^{2} x & \left(1+c^{2}\right) x \\ \left(1+a^{2}\right) x & \left(1+b^{2}\right) x & 1+c^{2} x\end{array}\right|\)
then \(f(x)\) is a polynomial of degree

79021 Matrix \(M_{r}\) is defined as \(M_{r}=\left[\begin{array}{cc}r & r-1 \\ r-1 & r\end{array}\right]\) \(r \in N\) Value of \(\operatorname{det}\left(M_{1}\right)+\operatorname{det}\left(M_{2}\right)+\operatorname{det}\left(M_{3}\right)+\) ... + det \(\left(\mathbf{M}_{2007}\right)\) is

79022 If \(y y^{2} 1+y^{3}=0\) then
\(\left|\begin{array}{lll}z & z^{2} & 1+z^{3}\end{array}\right|\)

79023 If \(\cos 2 \theta=0\), then
\(\left|\begin{array}{ccc}0 & \cos \theta & \sin \theta \\ \cos \theta & \sin \theta & 0 \\ \sin \theta & 0 & \cos \theta\end{array}\right|^{2}=\)

79020 If \(\mathbf{a}^{2}+b^{2}+c^{2}=-2\)
and \(f(x)=\left|\begin{array}{ccc}1+a^{2} x & \left(1+b^{2}\right) x & \left(1+c^{2}\right) x \\ \left(1+a^{2}\right) x & 1+b^{2} x & \left(1+c^{2}\right) x \\ \left(1+a^{2}\right) x & \left(1+b^{2}\right) x & 1+c^{2} x\end{array}\right|\)
then \(f(x)\) is a polynomial of degree

79021 Matrix \(M_{r}\) is defined as \(M_{r}=\left[\begin{array}{cc}r & r-1 \\ r-1 & r\end{array}\right]\) \(r \in N\) Value of \(\operatorname{det}\left(M_{1}\right)+\operatorname{det}\left(M_{2}\right)+\operatorname{det}\left(M_{3}\right)+\) ... + det \(\left(\mathbf{M}_{2007}\right)\) is

79022 If \(y y^{2} 1+y^{3}=0\) then
\(\left|\begin{array}{lll}z & z^{2} & 1+z^{3}\end{array}\right|\)

79023 If \(\cos 2 \theta=0\), then
\(\left|\begin{array}{ccc}0 & \cos \theta & \sin \theta \\ \cos \theta & \sin \theta & 0 \\ \sin \theta & 0 & \cos \theta\end{array}\right|^{2}=\)

79020 If \(\mathbf{a}^{2}+b^{2}+c^{2}=-2\)
and \(f(x)=\left|\begin{array}{ccc}1+a^{2} x & \left(1+b^{2}\right) x & \left(1+c^{2}\right) x \\ \left(1+a^{2}\right) x & 1+b^{2} x & \left(1+c^{2}\right) x \\ \left(1+a^{2}\right) x & \left(1+b^{2}\right) x & 1+c^{2} x\end{array}\right|\)
then \(f(x)\) is a polynomial of degree

79021 Matrix \(M_{r}\) is defined as \(M_{r}=\left[\begin{array}{cc}r & r-1 \\ r-1 & r\end{array}\right]\) \(r \in N\) Value of \(\operatorname{det}\left(M_{1}\right)+\operatorname{det}\left(M_{2}\right)+\operatorname{det}\left(M_{3}\right)+\) ... + det \(\left(\mathbf{M}_{2007}\right)\) is

79022 If \(y y^{2} 1+y^{3}=0\) then
\(\left|\begin{array}{lll}z & z^{2} & 1+z^{3}\end{array}\right|\)

79023 If \(\cos 2 \theta=0\), then
\(\left|\begin{array}{ccc}0 & \cos \theta & \sin \theta \\ \cos \theta & \sin \theta & 0 \\ \sin \theta & 0 & \cos \theta\end{array}\right|^{2}=\)