Name:      

Directions: Show all work. No credit for answers without work.

1. [4 points] Solve the following linear system. \[ \begin {array}{*{7}{r}} & & 2x_2 &+& x_3 &=& 1\\ -2x_1 &+& 17x_2 &+& 16x_3 &=& 1\\ x_1 &-& 8x_2 &-& 8x_3 &=& 1 \end {array} \]

2. [3 points] Give an example of an inconsistent linear system with two equations \(\mathrm {Eq1}\) and \(\mathrm {Eq2}\) such that each equation individually has infinitely many solutions.

3. [3 points] The following augmented matrix represents a linear system. Find all values for \(h\) that make the system consistent. (Hint: simplify the second and third rows as much as possible before involving \(h\) in your computation. Avoid fractions if possible.) \[ \left [ \begin {array}{*{3}{r}} -1 & h & 30\\ 5 & -2 & -24\\ 3 & 2 & 8 \end {array} \right ] \]