Linear Equations - Gaussian Elimination

Let

A = [\begin{matrix} 0 & 1 & 0 \\ 0 & 0 & 1 \\ 1 & 0 & 0 \end{matrix}]

and

B = [\begin{matrix} 1 & 0 & 0 \\ 0 & 3 & 1 \\ - 1 & 1 & 0 \end{matrix}]

. Both

A

and

B

can be transformed to the same matrix in reduced row-echelon form using elementary row operations.

The answer is “True”. Using Gauss-Jordan elimination, both matrices can be transformed to $[\begin{matrix} 1 & 0 & 0 \\ 0 & 1 & 0 \\ 0 & 0 & 1 \end{matrix}]$ .

To transform $A$ to this matrix, apply the following operations in the order given: $R_{1} \leftrightarrow R_{3}$ , $R_{2} \leftrightarrow R_{3}$ .

To transform $B$ , apply the following operations in the order given: $R_{3} \leftarrow R_{3} + R_{1}$ , $R_{2} \leftarrow R_{2} + (- 3) R_{3}$ , $R_{2} \leftrightarrow R_{3}$ .

Question