Solve the matrix equation for y. [1 2 -3] [12 31-² 2 6 3 12 x 0-1/1/20 O O There is no correct answer. -6 ³ [131] + [6
Solve the matrix equation for y. [1 2 -3] [12 31-² 2 6 3 12 x 0-1/1/20 O O There is no correct answer. -6 ³ [131] + [6
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
Related questions
Question
![### Matrix Equation Problem
#### Question:
Solve the matrix equation for \( y \).
\[
\begin{bmatrix}
1 & 2 & -3 \\
y & 4 & 1
\end{bmatrix}
- 2 \begin{bmatrix}
2 & 6 & 3 \\
1 & 2 & x
\end{bmatrix}
= 3 \begin{bmatrix}
1 & 3 & 7 \\
y & 1 & 1
\end{bmatrix}
+ \begin{bmatrix}
-6 & -19 & -30 \\
0 & -3 & 2
\end{bmatrix}
\]
##### Options:
- O \( 0 \)
- O \( -\frac{1}{2} \)
- O \( \frac{1}{2} \)
- O There is no correct answer.
- O \( -1 \)
#### Explanation:
This is a matrix equation involving addition, subtraction, and scalar multiplication of matrices. The task is to solve for the variable \( y \).
The given equation involves four matrices and requires carrying out matrix operations step by step. The error terms and constant entries provided along with multiple answer choices relating to different potential solutions are critical for determining the correct solution.
To solve for \( y \):
1. Perform scalar multiplication and addition/subtraction of corresponding elements in the matrices.
2. Compare the resulting elements to solve for the value of \( y \).
For a full understanding and solution process, one needs to apply the rules of matrix operations accurately.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F5ecf1484-f95f-4119-9858-43c8382b92c0%2Fe90dcd24-e5f3-4cba-b7f5-463d8dcd70e5%2F2unxcrcp_processed.jpeg&w=3840&q=75)
Transcribed Image Text:### Matrix Equation Problem
#### Question:
Solve the matrix equation for \( y \).
\[
\begin{bmatrix}
1 & 2 & -3 \\
y & 4 & 1
\end{bmatrix}
- 2 \begin{bmatrix}
2 & 6 & 3 \\
1 & 2 & x
\end{bmatrix}
= 3 \begin{bmatrix}
1 & 3 & 7 \\
y & 1 & 1
\end{bmatrix}
+ \begin{bmatrix}
-6 & -19 & -30 \\
0 & -3 & 2
\end{bmatrix}
\]
##### Options:
- O \( 0 \)
- O \( -\frac{1}{2} \)
- O \( \frac{1}{2} \)
- O There is no correct answer.
- O \( -1 \)
#### Explanation:
This is a matrix equation involving addition, subtraction, and scalar multiplication of matrices. The task is to solve for the variable \( y \).
The given equation involves four matrices and requires carrying out matrix operations step by step. The error terms and constant entries provided along with multiple answer choices relating to different potential solutions are critical for determining the correct solution.
To solve for \( y \):
1. Perform scalar multiplication and addition/subtraction of corresponding elements in the matrices.
2. Compare the resulting elements to solve for the value of \( y \).
For a full understanding and solution process, one needs to apply the rules of matrix operations accurately.
![**Question:**
For what value(s) of \( h \) are the following vectors linearly independent?
\[ \vec{v}_1 = \begin{bmatrix} 3 \\ 4 \\ -4 \end{bmatrix}, \quad \vec{v}_2 = \begin{bmatrix} -4 \\ 1 \\ 1 \end{bmatrix}, \quad \text{and} \quad \vec{v}_3 = \begin{bmatrix} h \\ -10 \\ 6 \end{bmatrix} \]
**Options:**
- \( \quad \circ h = 2 \)
- \( \quad \circ h \neq 2 \)
- \( \quad \circ h = -2 \)
- \( \quad \circ h = 2 \text{ or } h = -2 \)
**Diagram Description:**
The presented problem is a linear algebra question asking for the values of \( h \) such that three given vectors are linearly independent. The vectors are provided in column vector format. Four potential answers are listed as multiple-choice options.
**Answer Choices:**
- \( h = 2 \)
- \( h \neq 2 \)
- \( h = -2 \)
- \( h = 2 \text{ or } h = -2 \)
This question would typically be solved by setting the determinant of the matrix formed by the vectors equal to zero, as the vectors are linearly independent if and only if the determinant of the matrix is non-zero.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F5ecf1484-f95f-4119-9858-43c8382b92c0%2Fe90dcd24-e5f3-4cba-b7f5-463d8dcd70e5%2Fbvg1ppm_processed.jpeg&w=3840&q=75)
Transcribed Image Text:**Question:**
For what value(s) of \( h \) are the following vectors linearly independent?
\[ \vec{v}_1 = \begin{bmatrix} 3 \\ 4 \\ -4 \end{bmatrix}, \quad \vec{v}_2 = \begin{bmatrix} -4 \\ 1 \\ 1 \end{bmatrix}, \quad \text{and} \quad \vec{v}_3 = \begin{bmatrix} h \\ -10 \\ 6 \end{bmatrix} \]
**Options:**
- \( \quad \circ h = 2 \)
- \( \quad \circ h \neq 2 \)
- \( \quad \circ h = -2 \)
- \( \quad \circ h = 2 \text{ or } h = -2 \)
**Diagram Description:**
The presented problem is a linear algebra question asking for the values of \( h \) such that three given vectors are linearly independent. The vectors are provided in column vector format. Four potential answers are listed as multiple-choice options.
**Answer Choices:**
- \( h = 2 \)
- \( h \neq 2 \)
- \( h = -2 \)
- \( h = 2 \text{ or } h = -2 \)
This question would typically be solved by setting the determinant of the matrix formed by the vectors equal to zero, as the vectors are linearly independent if and only if the determinant of the matrix is non-zero.
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