**Determine if the following matrix is in reduced form**If not, indicate the row operation(s) necessary to transform the matrix into reduced form.\[ \begin{pmatrix} 1 & 0 & 3 & 2 \\0 & 0 & 0 & 0 \\0 & 1 & 5 & 4 \end{pmatrix} \]The matrix ❏ in reduced form.**Which row operation is necessary to transform the matrix into reduced form?****Options:**A. $ R_2 \leftrightarrow R_3 $B. $ R_1 \leftrightarrow R_2 $C. $ R_1 \leftrightarrow R_3 $D. No row operations are necessary, the matrix is in reduced form.**Explanation:**The problem presents a 3x4 matrix and asks whether it is already in reduced form. If it is not in reduced form, you are asked to identify which row operation would transform it into reduced form from the options given.**Analysis of the Matrix:**- **Row operations:** - $R_2 \leftrightarrow R_3$: Swap row 2 and row 3. - $R_1 \leftrightarrow R_2$: Swap row 1 and row 2. - $R_1 \leftrightarrow R_3$: Swap row 1 and row 3.The correct choice will correctly align the pivot positions and ensure the matrix is in reduced row echelon form, where each leading entry in a row is 1 and is the only non-zero entry in its column.

Answered: Image /qna-images/answer/13cc1e81-18a2-4b63-9265-4d6bd6cd80b8.jpg

Determine if the following matrix is in reduced form. If not, indicate the row operation(s) necessary to transform the matrix into reduced form. 10 3 2 0 0 0 0 0154 The matrix in reduced form. Which row operation is necessary to transform the matrix into reduced form? O A. R2++R3 O B. R, ++R2 OC. R,++R3 O D. No row operations are necessary, the matrix is in reduced form.

Determine if the following matrix is in reduced form. If not, indicate the row operation(s) necessary to transform the matrix into reduced form. 10 3 2 0 0 0 0 0154 The matrix in reduced form. Which row operation is necessary to transform the matrix into reduced form? O A. R2++R3 O B. R, ++R2 OC. R,++R3 O D. No row operations are necessary, the matrix is in reduced form.

Advanced Engineering Mathematics

10th Edition

ISBN:9780470458365

Author:Erwin Kreyszig

Publisher:Erwin Kreyszig

Chapter2: Second-order Linear Odes

Section: Chapter Questions

Problem 1RQ

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Question

**Determine if the following matrix is in reduced form**

If not, indicate the row operation(s) necessary to transform the matrix into reduced form.

\[ \begin{pmatrix}
1 & 0 & 3 & 2 \\
0 & 0 & 0 & 0 \\
0 & 1 & 5 & 4
\end{pmatrix} \]

The matrix ❏ in reduced form.

**Which row operation is necessary to transform the matrix into reduced form?**

**Options:**

A. $ R_2 \leftrightarrow R_3 $

B. $ R_1 \leftrightarrow R_2 $

C. $ R_1 \leftrightarrow R_3 $

D. No row operations are necessary, the matrix is in reduced form.

**Explanation:**

The problem presents a 3x4 matrix and asks whether it is already in reduced form. If it is not in reduced form, you are asked to identify which row operation would transform it into reduced form from the options given.

**Analysis of the Matrix:**

- **Row operations:**
- $R_2 \leftrightarrow R_3$: Swap row 2 and row 3.
- $R_1 \leftrightarrow R_2$: Swap row 1 and row 2.
- $R_1 \leftrightarrow R_3$: Swap row 1 and row 3.

The correct choice will correctly align the pivot positions and ensure the matrix is in reduced row echelon form, where each leading entry in a row is 1 and is the only non-zero entry in its column.

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