Consider the system of linear equations \( \begin{array}{l}x+y-z=2 \\ 3 x+2 y-z=3 \\ -x-y+2 z=-1\end{array} \) Write down the system in matrix form, \( A X=b \) where \( X=\left[\begin{array}{l}x \\ y \\ z\end{array}\right] \) Write down the coefficient matrix \( A \) of the above system. Determine the inverse \( A^{-1} \) of \( A \) by applying the matrix inverse algorithm, that is by applying the sequence of elementary row operations in the sense \( \left[A \mid I_{3}\right] \) where. \( I_{3} \) is the 3 by 3 identity matrix.

\( \left.\begin{array}{l}\left.\text { 1) } \begin{array}{l}\left(4 x^{2}+5\right)\left(x^{2}-2\right)\left(x^{2}+2\right)=0 \\ \text { A) }\left\{\begin{array}{l}i \sqrt{5} \\ 2\end{array}-\frac{i \sqrt{5}}{2}, \sqrt{2},-\sqrt{2}, i \sqrt{2},-i \sqrt{2}\right. \\ \text { B) }\left\{\frac{i \sqrt{10}}{2},-\frac{i \sqrt{10}}{2}, \sqrt{2},-\sqrt{2}, i \sqrt{2},-i \sqrt{2}\right.\end{array}\right\} \\ \text { C) }\left\{\frac{i \sqrt{15}}{3},-\frac{i \sqrt{15}}{3}, i \sqrt{3},-i \sqrt{3}, i \sqrt{2},-i \sqrt{2}\right.\end{array}\right\} \)

Watch the video that describes performing vector operations. Click here to watch the video. Given vectors \( \mathbf{u} \) and \( \mathbf{v} \), find \( \mathbf{( a )} 9 \mathbf{u}=\langle 9,9\rangle, \mathbf{v}=\langle 6,0\rangle \) (b) \( 9 \mathbf{u}+6 \mathbf{v} \) (c) \( \mathbf{v}-6 \mathbf{u} \). \( \begin{array}{ll}\text { (a) } 9 \mathbf{u}=\langle 81,81\rangle \\ \text { (b) } 9 \mathbf{u}+6 \mathbf{v}=\langle\square, \square\rangle\end{array} \)

\( 1 \leftarrow \quad \) Given vectors \( \mathbf{u} \) and \( \mathbf{v} \), find (a) \( 7 \mathbf{u} \) \( \mathbf{u}=6 \mathbf{i}, \mathbf{v}=3 \mathbf{i}+6 \mathbf{j} \) (b) \( 7 \mathbf{u}+2 \mathbf{v} \) (c) \( \mathbf{v}-2 \mathbf{u} \). (a) \( 7 \mathbf{u}=42 \mathbf{i} \) (Type your answer in terms of iand \( \mathbf{j} \).) (b) \( 7 \mathbf{u}+2 \mathbf{v}=\square \) (Type your answer in terms of \( \mathbf{i} \) and \( \mathbf{j} \).)

Find the zeros for the polynomial function and give the multiplicity for each zero. State whether the graph crosses the \( x \)-axis or touches the \( x \)-axis and turns around at each zero. \( f(x)=x^{3}+3 x^{2}-16 x-48 \) Determine the behavior of the function at each zero. Select the correct choice below and, if necessary, fill in the answer boxes within your choice. A. The graph crosses the \( x \)-axis at \( x=\square \). The graph touches the \( x \)-axis and turns around at \( x=\square \). (Type integers or decimals. Simplify your answers. Use a comma to separate answers as needed.) B. The graph crosses the \( x \)-axis at all zeros. C. The graph touches the \( x \)-axis and turns around at all zeros.

dation \( \log _{3}(2 x-1)=3 \)