Question 3 Solve the problem. 1-3 21 Let A--2 5-1 and b = b2 3-6-3 Determine if the equation Ax-b is consistent for all possible b₁,b2, b3. If the equation is not consistent for all possible by, by by give a description of the set of all b for which the equation is consistent (i.e., a condition which must be satisfied by by, by by } O Equation is consistent for all possible by, b₂. b3. O Equation is consistent for all b₁,b2, b3 satisfying -3b₁ + b3 = 0. O Equation is consistent for all b₁,b₂, b3 satisfying 3b₁ + 3b₂+ b3 = 0. O Equation is consistent for all b₁,b₂, b3 satisfying -b₁ + b₂ + b3 = 0. « Previous Next- Quiz saved at 3:37am Submit Qui
Question 3 Solve the problem. 1-3 21 Let A--2 5-1 and b = b2 3-6-3 Determine if the equation Ax-b is consistent for all possible b₁,b2, b3. If the equation is not consistent for all possible by, by by give a description of the set of all b for which the equation is consistent (i.e., a condition which must be satisfied by by, by by } O Equation is consistent for all possible by, b₂. b3. O Equation is consistent for all b₁,b2, b3 satisfying -3b₁ + b3 = 0. O Equation is consistent for all b₁,b₂, b3 satisfying 3b₁ + 3b₂+ b3 = 0. O Equation is consistent for all b₁,b₂, b3 satisfying -b₁ + b₂ + b3 = 0. « Previous Next- Quiz saved at 3:37am Submit Qui
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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Transcribed Image Text:**Question 3**
Solve the problem.
Let \( A = \begin{bmatrix} 1 & -3 & 2 \\ -2 & 5 & -1 \\ 3 & -6 & -3 \end{bmatrix} \) and \( b = \begin{bmatrix} b_1 \\ b_2 \\ b_3 \end{bmatrix} \).
Determine if the equation \( Ax = b \) is consistent for all possible \( b_1, b_2, b_3 \). If the equation is not consistent for all possible \( b_1, b_2, b_3 \), give a description of the set of all \( b \) for which the equation is consistent (i.e., a condition which must be satisfied by \( b_1, b_2, b_3 \)).
- ⭕ Equation is consistent for all possible \( b_1, b_2, b_3 \).
- ⭕ Equation is consistent for all \( b_1, b_2, b_3 \) satisfying \( -3b_1 + b_3 = 0 \).
- ⭕ Equation is consistent for all \( b_1, b_2, b_3 \) satisfying \( 3b_1 + 3b_2 + b_3 = 0 \).
- ⭕ Equation is consistent for all \( b_1, b_2, b_3 \) satisfying \( -b_1 + b_2 + b_3 = 0 \).
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![### Question 3
**Solve the problem.**
Given:
\[ A = \begin{bmatrix} 1 & -3 & 2 \\ -2 & 5 & -1 \\ 3 & -6 & -3 \end{bmatrix} \]
and
\[ b = \begin{bmatrix} b_1 \\ b_2 \\ b_3 \end{bmatrix} \]
Determine if the equation \( Ax = b \) is consistent for all possible \( b_1, b_2, b_3 \). If the equation is not consistent for all possible \( b_1, b_2, b_3 \), give a description of the set of all \( b \) for which the equation is consistent (i.e., a condition which must be satisfied by \( b_1, b_2, b_3 \)).
#### Options:
- **(A)** Equation is consistent for all possible \( b_1, b_2, b_3 \).
- **(B)** Equation is consistent for all \( b_1, b_2, b_3 \) satisfying \( -3b_1 + b_3 = 0 \).
- **(C)** Equation is consistent for all \( b_1, b_2, b_3 \) satisfying \( 3b_1 + 3b_2 + b_3 = 0 \).
- **(D)** Equation is consistent for all \( b_1, b_2, b_3 \) satisfying \( -b_1 + b_2 + b_3 = 0 \).
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Transcribed Image Text:### Question 3
**Solve the problem.**
Given:
\[ A = \begin{bmatrix} 1 & -3 & 2 \\ -2 & 5 & -1 \\ 3 & -6 & -3 \end{bmatrix} \]
and
\[ b = \begin{bmatrix} b_1 \\ b_2 \\ b_3 \end{bmatrix} \]
Determine if the equation \( Ax = b \) is consistent for all possible \( b_1, b_2, b_3 \). If the equation is not consistent for all possible \( b_1, b_2, b_3 \), give a description of the set of all \( b \) for which the equation is consistent (i.e., a condition which must be satisfied by \( b_1, b_2, b_3 \)).
#### Options:
- **(A)** Equation is consistent for all possible \( b_1, b_2, b_3 \).
- **(B)** Equation is consistent for all \( b_1, b_2, b_3 \) satisfying \( -3b_1 + b_3 = 0 \).
- **(C)** Equation is consistent for all \( b_1, b_2, b_3 \) satisfying \( 3b_1 + 3b_2 + b_3 = 0 \).
- **(D)** Equation is consistent for all \( b_1, b_2, b_3 \) satisfying \( -b_1 + b_2 + b_3 = 0 \).
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