Find the transpose of

$$A=\left[\begin{array}{rrr} -1 & 0 & 3 \\ 2 & 1 & -4 \end{array}\right].$$

Reduce the system of linear equations to upper triangular form and solve.

$$\begin{aligned} 2 x+3 y &=5 \\ -y &=-2+\frac{2}{3} x \end{aligned}$$

Find the transpose of

$$A=\left[\begin{array}{r} 2 \\ -3 \\ 5 \end{array}\right].$$

Normalize $[0,-3,1,3]^{\prime}[0,-3,1,3]^{\prime}.$

Suppose a vector

$$\left[\begin{array}{l} x_{1} \\ x_{2} \end{array}\right]$$

has length 2 and is $140^{\circ}$ clockwise from the positive $x_{1}$-axis. Find $x_{1}$ and $x_{2}.$

Show that the eigenvalues of

$$\left[\begin{array}{ll} a & 0 \\ c & b \end{array}\right]$$

are equal to a and b.