Describe the possible echelon forms of the standard matrix for a linear transformation T where T: R4 →R³ is onto. Give some examples of the echelon forms. The leading entries, denoted may have any nonzero value; the starred entries, denoted *, may have any value (including zero). Select all that apply. ☐A. D. 0 * 00 0 0 0 0 0 0 0 0■ 0 0 0 0 0 0 0 * * 0 00 * OL * * * * [ B. * * * C. 0 0 0 0 0 0000 0 0 0 0 * F. 0 * DEN * * 0 0 * 0 0 0 01. * * 0 H. 00 E. 0 0 0 * * * 0000 000 *
Describe the possible echelon forms of the standard matrix for a linear transformation T where T: R4 →R³ is onto. Give some examples of the echelon forms. The leading entries, denoted may have any nonzero value; the starred entries, denoted *, may have any value (including zero). Select all that apply. ☐A. D. 0 * 00 0 0 0 0 0 0 0 0■ 0 0 0 0 0 0 0 * * 0 00 * OL * * * * [ B. * * * C. 0 0 0 0 0 0000 0 0 0 0 * F. 0 * DEN * * 0 0 * 0 0 0 01. * * 0 H. 00 E. 0 0 0 * * * 0000 000 *
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
![**Topic: Possible Echelon Forms of the Standard Matrix for a Linear Transformation**
**Description:**
Describe the possible echelon forms of the standard matrix for a linear transformation \( T \) where \( T: \mathbb{R}^4 \to \mathbb{R}^3 \) is onto.
---
**Echelon Form Examples:**
The leading entries, denoted by ■, may have any nonzero value; the starred entries, denoted by *, may have any value (including zero). Select all that apply.
**Matrices:**
- **A.**
\[
\begin{bmatrix}
\blacksquare & * & * & * \\
0 & \blacksquare & * & * \\
0 & 0 & \blacksquare & * \\
\end{bmatrix}
\]
- **B.**
\[
\begin{bmatrix}
\blacksquare & * & * & * \\
0 & 0 & \blacksquare & * \\
0 & 0 & 0 & \blacksquare \\
\end{bmatrix}
\]
- **C.**
\[
\begin{bmatrix}
0 & 0 & 0 & \blacksquare \\
0 & 0 & 0 & 0 \\
0 & 0 & 0 & 0 \\
\end{bmatrix}
\]
- **D.**
\[
\begin{bmatrix}
\blacksquare & * & * & * \\
0 & \blacksquare & 0 & * \\
0 & 0 & \blacksquare & * \\
\end{bmatrix}
\]
- **E.**
\[
\begin{bmatrix}
0 & \blacksquare & 0 & * \\
0 & 0 & \blacksquare & * \\
0 & 0 & 0 & \blacksquare \\
\end{bmatrix}
\]
- **F.**
\[
\begin{bmatrix}
\blacksquare & * & * & * \\
0 & 0](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F46029127-96a5-4dc2-997a-3c090d1aab2d%2F83450ee5-2a32-4c1d-af61-3b4572758c03%2Ft23jojf_processed.png&w=3840&q=75)
Transcribed Image Text:**Topic: Possible Echelon Forms of the Standard Matrix for a Linear Transformation**
**Description:**
Describe the possible echelon forms of the standard matrix for a linear transformation \( T \) where \( T: \mathbb{R}^4 \to \mathbb{R}^3 \) is onto.
---
**Echelon Form Examples:**
The leading entries, denoted by ■, may have any nonzero value; the starred entries, denoted by *, may have any value (including zero). Select all that apply.
**Matrices:**
- **A.**
\[
\begin{bmatrix}
\blacksquare & * & * & * \\
0 & \blacksquare & * & * \\
0 & 0 & \blacksquare & * \\
\end{bmatrix}
\]
- **B.**
\[
\begin{bmatrix}
\blacksquare & * & * & * \\
0 & 0 & \blacksquare & * \\
0 & 0 & 0 & \blacksquare \\
\end{bmatrix}
\]
- **C.**
\[
\begin{bmatrix}
0 & 0 & 0 & \blacksquare \\
0 & 0 & 0 & 0 \\
0 & 0 & 0 & 0 \\
\end{bmatrix}
\]
- **D.**
\[
\begin{bmatrix}
\blacksquare & * & * & * \\
0 & \blacksquare & 0 & * \\
0 & 0 & \blacksquare & * \\
\end{bmatrix}
\]
- **E.**
\[
\begin{bmatrix}
0 & \blacksquare & 0 & * \\
0 & 0 & \blacksquare & * \\
0 & 0 & 0 & \blacksquare \\
\end{bmatrix}
\]
- **F.**
\[
\begin{bmatrix}
\blacksquare & * & * & * \\
0 & 0
Expert Solution
Step 1
Answer)
Possible echelon forms are :A, F, G, I
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