Question

Perform each matrix row operation and write the new matrix.﻿[1−111∣301−2−1∣02034∣115124∣6]−2R1+R3−5R1+R4\begin{bmatrix}
1 & -1 & 1 & 1 & \vert & 3 \
0 & 1 & -2 & -1 & \vert & 0 \
2 & 0 & 3 & 4 & \vert & 11 \
5 & 1 & 2 & 4 & \vert & 6
\end{bmatrix}
\quad
\begin{array}{l}
-2R_1 + $$R_3$$ \
-5R_1 + $$R_4$$
\end{array}​1025​−1101​1−232​1−144​∣∣∣∣​30116​​−2R1​+R3​−5R1​+R4​​

Accepted Answer

Identify the given matrix and the row operations to perform. The matrix is:

$$\left[\begin{array}{cccc|c} 1 & -1 & 1 & 1 & 3 \ 0 & 1 & -2 & -1 & 0 \ 2 & 0 & 3 & 4 & 11 \ 5 & 2 & 4 & 6 & 6 \end{array}ight]$$

and the row operations are:

$$-2R_1 + R_3$$
$$-5R_1 + R_4$$ Perform the first row operation: replace row 3 ($$R_3) $$with $$-2$$ times row 1 plus row 3. Calculate each element of the new row 3 by multiplying each element of row 1 by $$-2$$ and then adding the corresponding element of row 3. Perform the second row operation: replace row 4 ($$R_4) $$with $$-5$$ times row 1 plus row 4. Calculate each element of the new row 4 by multiplying each element of row 1 by $$-5$$ and then adding the corresponding element of row 4. Write the new matrix after these row operations, keeping rows 1 and 2 unchanged, and rows 3 and 4 updated with the results from the previous steps. Double-check each element in the new rows 3 and 4 to ensure the arithmetic was done correctly, confirming the accuracy of the row operations.

Perform each matrix row operation and write the new matrix.
$\begin{bmatrix}\)1 & -1 & 1 & 1 & \(\vert\) & 3 \\0 & 1 & -2 & -1 & \(\vert\) & 0 \\2 & 0 & 3 & 4 & \(\vert\) & 11 \\5 & 1 & 2 & 4 & \(\vert\) & 6\(\end{bmatrix}\[\quad\]\begin{array}{l}\)-2R_1 + R_3 \\-5R_1 + R_4\(\end{array}$

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Key Concepts

Matrix Row Operations

Performing Linear Combinations of Rows

Augmented Matrices and Systems of Equations