Question

Let \( A=\left(\begin{array}{ccc}0 & 0 & 1 \\ 1 & 0 & -4 \\ -4 & 1 & -2\end{array}\right) \) and \( \mathbf{b}=\left(\begin{array}{c}-1 \\ -1 \\ -3\end{array}\right) \). The matrix equation \( A\left(\begin{array}{c}x \\ y \\ z\end{array}\right)=\mathbf{b} \) has a unique solution. By putting \( (A \mid \mathbf{b}) \) into row reduced echelon form, find this solution.

          Let \( A=\left(\begin{array}{ccc}0 & 0 & 1 \\ 1 & 0 & -4 \\ -4 & 1 & -2\end{array}\right) \) and \( \mathbf{b}=\left(\begin{array}{c}-1 \\ -1 \\ -3\end{array}\right) \).
The matrix equation \( A\left(\begin{array}{c}x \\ y \\ z\end{array}\right)=\mathbf{b} \) has a unique solution. By putting \( (A \mid \mathbf{b}) \) into row reduced echelon form, find this solution.

Let A=(
0 0 1
1 0 -4
-4 1 -2
) and 𝐛=(
-1
-1
-3
).
The matrix equation A(
x
y
z
)=𝐛 has a unique solution. By putting (A |𝐛) into row reduced echelon form, find this solution.

Added by Felix H.

Differential Equations and Linear Algebra

Stephen W. Goode, Scott A. Annin 4th Edition

Instant Answer

Solved by Expert Likhit Ganedi

Step 1

\[ \left(\begin{array}{ccc|c} 0 & 0 & 1 & -1 \\ 1 & 0 & -4 & -1 \\ -4 & 1 & -2 & -3 \end{array}\right) \] Show more…

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Let \( A=\left(\begin{array}{ccc}0 & 0 & 1 \\ 1 & 0 & -4 \\ -4 & 1 & -2\end{array}\right) \) and \( \mathbf{b}=\left(\begin{array}{c}-1 \\ -1 \\ -3\end{array}\right) \). The matrix equation \( A\left(\begin{array}{c}x \\ y \\ z\end{array}\right)=\mathbf{b} \) has a unique solution. By putting \( (A \mid \mathbf{b}) \) into row reduced echelon form, find this solution.