form of the augmented matrix of the matrix equation $$ A \boldsymbol{x}=\boldsymbol{b} $$ (Hint: You can find the solution in the slide of Week 2 , but I still suggest that you do it once again), and do the following: (1) Record each step (the row operation) with a matrix. (2) Suppose you get $$ t $$ matrices $$ M_{1}, M_{2}, \ldots, M_{t} $$ in order (you may name it with other names), then (a) Compute $$ E=M_{t} M_{t-1} \cdots M_{2} M_{1} $$ (Notice the order); (b) Compute $$ E A $$, and check that if it is an identity matrix. (c) Compute $$ E \boldsymbol{b} $$, and check that if it equals to the last column vector in the RREF of the augmented matrix.

Question

Donnelly Powers · Accepted Answer

1. Form the augmented matrix $$[A | \boldsymbol{b}]$$. 2. Perform row operations to reach reduced row echelon form (RREF). 3. Compute the product of the row operation matrices $$ E $$. 4. Verify $$ E A = I $$ and $$ E \boldsymbol{b} $$ equals the last column of the RREF.

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