Solved on Nov 15, 2023

Perform the given row operations on the provided $2 \times 3$ matrix.

STEP 1

Assumptions1. We are given ax3 matrix. . The row operations are performed on this matrix.
3. The row operation (a) is not specified.
4. The row operation (b) is to multiply the second row (R) by1/3.
5. The row operation (c) is to multiply the first row (R1) by -3 and then add it to the second row (R).

STEP 2

Perform the row operation (b) on the given matrix. This operation is to multiply the second row (R2) by1/.
$\left(\frac{1}{}\right) R2 \rightarrow R2$

STEP 3

Apply the operation to the second row of the matrix.
$\left[\begin{array}{rr|r} 1 & -1 &9 \\ (1/3)3 & (1/3)-6 & (1/3)*18\end{array}\right]$

STEP 4

Calculate the new values for the second row.
$\left[\begin{array}{rr|r} 1 & -1 &9 \\ 1 & -2 &6\end{array}\right]$

STEP 5

Perform the row operation (c) on the matrix obtained in4. This operation is to multiply the first row (R1) by -3 and then add it to the second row (R2).
$(-3) R1+R2 \rightarrow R2$

STEP 6

Apply the operation to the rows of the matrix.
$\left[\begin{array}{rr|r} 1 & -1 &9 \\ (-3)1 +1 & (-3)-1 + -2 & (-3)*9 +6\end{array}\right]$

STEP 7

Calculate the new values for the second row.
$\left[\begin{array}{rr|r} 1 & -1 &9 \\ -2 &1 & -21\end{array}\right]$ The matrix after performing the indicated row operations is $\left[\begin{array}{rr|r} 1 & -1 &9 \\ -2 &1 & -21\end{array}\right]$

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Perform the given row operations on the provided $2 \times 3$ matrix.

STEP 1

STEP 2

Perform the row operation (b) on the given matrix. This operation is to multiply the second row (R2) by1/.
$\left(\frac{1}{}\right) R2 \rightarrow R2$

STEP 3

Apply the operation to the second row of the matrix.
$\left[\begin{array}{rr|r} 1 & -1 &9 \\ (1/3)3 & (1/3)-6 & (1/3)*18\end{array}\right]$

STEP 4

Calculate the new values for the second row.
$\left[\begin{array}{rr|r} 1 & -1 &9 \\ 1 & -2 &6\end{array}\right]$

STEP 5

Perform the row operation (c) on the matrix obtained in4. This operation is to multiply the first row (R1) by -3 and then add it to the second row (R2).
$(-3) R1+R2 \rightarrow R2$

STEP 6

Apply the operation to the rows of the matrix.
$\left[\begin{array}{rr|r} 1 & -1 &9 \\ (-3)1 +1 & (-3)-1 + -2 & (-3)*9 +6\end{array}\right]$

STEP 7

Calculate the new values for the second row.
$\left[\begin{array}{rr|r} 1 & -1 &9 \\ -2 &1 & -21\end{array}\right]$ The matrix after performing the indicated row operations is $\left[\begin{array}{rr|r} 1 & -1 &9 \\ -2 &1 & -21\end{array}\right]$

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Perform the given row operations on the provided 2×32 \times 32×3 matrix.

STEP 1

Assumptions1. We are given ax3 matrix. . The row operations are performed on this matrix.3. The row operation (a) is not specified.4. The row operation (b) is to multiply the second row (R) by1/3.5. The row operation (c) is to multiply the first row (R1) by -3 and then add it to the second row (R).

STEP 2

Perform the row operation (b) on the given matrix. This operation is to multiply the second row (R2) by1/.(1)R2→R2\left(\frac{1}{}\right) R2 \rightarrow R2(1​)R2→R2

STEP 3

Apply the operation to the second row of the matrix.[1−19(1/3)∗3(1/3)∗−6(1/3)∗18]\left[\begin{array}{rr|r} 1 & -1 &9 \\ (1/3)*3 & (1/3)*-6 & (1/3)*18\end{array}\right] [1(1/3)∗3​−1(1/3)∗−6​9(1/3)∗18​]

STEP 4

Calculate the new values for the second row.[1−191−26]\left[\begin{array}{rr|r} 1 & -1 &9 \\ 1 & -2 &6\end{array}\right] [11​−1−2​96​]

STEP 5

Perform the row operation (c) on the matrix obtained in4. This operation is to multiply the first row (R1) by -3 and then add it to the second row (R2).(−3)R1+R2→R2(-3) R1+R2 \rightarrow R2(−3)R1+R2→R2

STEP 6

Apply the operation to the rows of the matrix.[1−19(−3)∗1+1(−3)∗−1+−2(−3)∗9+6]\left[\begin{array}{rr|r} 1 & -1 &9 \\ (-3)*1 +1 & (-3)*-1 + -2 & (-3)*9 +6\end{array}\right] [1(−3)∗1+1​−1(−3)∗−1+−2​9(−3)∗9+6​]

STEP 7

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Perform the given row operations on the provided $2 \times 3$ matrix.

Perform the row operation (b) on the given matrix. This operation is to multiply the second row (R2) by1/.
$\left(\frac{1}{}\right) R2 \rightarrow R2$

Apply the operation to the second row of the matrix.
$\left[\begin{array}{rr|r} 1 & -1 &9 \\ (1/3)3 & (1/3)-6 & (1/3)*18\end{array}\right]$

Calculate the new values for the second row.
$\left[\begin{array}{rr|r} 1 & -1 &9 \\ 1 & -2 &6\end{array}\right]$

Perform the row operation (c) on the matrix obtained in4. This operation is to multiply the first row (R1) by -3 and then add it to the second row (R2).
$(-3) R1+R2 \rightarrow R2$

Apply the operation to the rows of the matrix.
$\left[\begin{array}{rr|r} 1 & -1 &9 \\ (-3)1 +1 & (-3)-1 + -2 & (-3)*9 +6\end{array}\right]$