Reduced Row Echelon Form Worksheet with Answer Key

What's on the worksheet

1. Let A = \begin{bmatrix} 1 & 2 & -5 & 2 & 1 \\ 2 & 5 & -12 & 2 & -5 \\ -2 & -2 & 6 & -7 & -14 \end{bmatrix} with columns a_1, , a_5.
2. Let A = \begin{bmatrix} 1 & 2 & -1 & 3 \\ 3 & 7 & 1 & 8 \end{bmatrix} \qquad B = \begin{bmatrix} 5 & 11 & -1 & 14 \\ 4 & 9 & 0 & 11 \end{bmatrix}
3. Let u_1 = (2, -1, 1), u_2 = (1, 1, -2), u_3 = (3, 0, -1) and u_4 = (-3, 3, -4).
4. A classmate says the reduced row echelon form of A = \begin{bmatrix} 2 & -4 & 1 & 3 & 0 \\ 1 & -2 & 1 & 1 & 1 \\ 3 & -6 & 0 & 6 & -3 \end{bmatrix}…
5. Let A = \begin{bmatrix} 1 & 1 & 1 & 2 \\ 2 & 3 & 5 & 4 \\ -1 & 0 & 2 & -1 \\ 1 & 2 & 4 & 3 \end{bmatrix} and b_1 = (3, 7, -1, 5), b_2 = (1, 0, 0,…
6. A 3 × 4 matrix A with columns a_1, a_2, a_3, a_4 has reduced row echelon form R = \begin{bmatrix} 1 & 2 & 0 & 1 \\ 0 & 0 & 1 & 3 \\ 0 & 0 & 0 & 0…