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

Simplify the expression. Assume that the variable is unrestricted and use absolute value symbols when necessary. \[ \sqrt{y^{2}-2 y+1} \]

Use the Factor Theorem to determine whether \( x-2 \) is a factor of \( P(x)=x^{3}-3 x^{2}-4 x+ \) Specifically, evaluate \( P \) at the proper value, and then determine whether \( x-2 \) is a factor. \( \begin{array}{l}P(\square)=\square \\ x-2 \text { is a factor of } P(x) \\ x-2 \text { is not a factor of } P(x)\end{array} \)

Multiply. \[ \begin{array}{l}(\sqrt{2}+7 \sqrt{5})(6 \sqrt{5}+\sqrt{2}) \\ \text { Simplify your answer as much as possible. }\end{array} \] II .

\( \begin{array}{l}\text { Ecuaciones Hultipicat } \\ \frac{9 x+3}{6}\end{array}=2 \)

Simplify the expression. Assume that the variable is unrestricted and use absolute value symbols when necessary. \[ \sqrt{25 y^{6}} \]