Question

b. a 5 x 4 matrix that is in reduced row echelon form.

Explanation:

Step1: Recall RREF requirements

A reduced row echelon form (RREF) matrix must satisfy:

1. All zero rows are at the bottom.
2. The leading entry (pivot) of a non-zero row is 1.
3. Each pivot is to the right of the pivot in the row above it.
4. All entries above and below a pivot are 0.

Step2: Construct 5x4 RREF matrix

We have 5 rows, 4 columns. We can have up to 4 pivots (one per column), with one zero row at the bottom.

$$\begin{bmatrix} 1 & 0 & 0 & 0 \\ 0 & 1 & 0 & 0 \\ 0 & 0 & 1 & 0 \\ 0 & 0 & 0 & 1 \\ 0 & 0 & 0 & 0 \end{bmatrix}$$

Answer:

$$\begin{bmatrix} 1 & 0 & 0 & 0 \\ 0 & 1 & 0 & 0 \\ 0 & 0 & 1 & 0 \\ 0 & 0 & 0 & 1 \\ 0 & 0 & 0 & 0 \end{bmatrix}$$

(Note: Any 5x4 matrix meeting RREF criteria is valid; this is one example.)