Haynes Logan

08/18/2023 · escuela secundaria

2. Let \( A=\left[\begin{array}{ccc}0 & -7 & -4 \\ 2 & 4 & 6 \\ 3 & 1 & -1\end{array}\right] \) and \( \boldsymbol{b}=\left[\begin{array}{c}2 \\ 12 \\ -2\end{array}\right] \). Find the reduced row echelon 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.