1. Determine which of the following equations is linear.
1
(a) \frac{1}{x} + 2y = 11, (b) $e^{-y} = -1$, (c) $x = -2z + 3x - y$, (d) $x + 5y - \sqrt{2}z = 1$, (e) $x + y^{-2} - 2z = 12$,
(f) $-x - y - z = -1$, (g) $xy - z = 1$, (h) $cos(\frac{\pi}{7})x - 3y + z = log3$, (i) $\frac{7}{2}cos x + y - 2z = 11$.
2. Write the coefficient matrix and the augmented matrix of each of the following systems.
$\begin{cases} x - 3y = 1 \\ 2x + 2y = 4 \end{cases}$
(a)
$\begin{cases} x + 2y - 2z = 3 \\ 3x - y + z = 1 \\ -x + 5y - 5z = 5 \end{cases}$
(b)
$\begin{cases} 2x_1 - 4x_2 - x_3 - x_4 = 1 \\ x_1 - 3x_2 + x_3 + 2x_4 = 2 \\ 3x_1 - 4x_2 - 3x_3 \\ = -3 \end{cases}$
(c)
3. Solve the following systems. Use the specified method.
$\begin{cases} x - y = 5 \\ -3x + 11y = 1 \end{cases}$
(a)
$\begin{cases} x + y + 2z = 8 \\ -x - 2y + 3z = 1 \\ 3x - 7y + 4z = 10 \end{cases}$
(b)
(substitution)
(Gaussian Elimination)
