Solve for x, y, and z. 2x + 2 16 (6 - y) -y 4 y z 3y -4z 20 16 X = = Z
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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![Certainly! Below is a transcription of the image content suitable for an educational website:
---
**Solve for \( x \), \( y \), and \( z \).**
\[
4 \begin{bmatrix} x & y \\ y & z \end{bmatrix} + 2 \begin{bmatrix} 2x & -y \\ 3y & -4z \end{bmatrix} = \begin{bmatrix} 16 & (6 - y) \\ 20 & 16 \end{bmatrix}
\]
**Calculate:**
\[ x = \_\_\_\_ \]
\[ y = \_\_\_\_ \]
\[ z = \_\_\_\_ \]
---
**Explanation of the Equation:**
1. The problem is a system of matrix equations. It involves finding the variables \( x \), \( y \), and \( z \) that satisfy the given equality.
2. The equation consists of three matrices:
- The first matrix is multiplied by the scalar 4:
\[
\begin{bmatrix} x & y \\ y & z \end{bmatrix}
\]
- The second matrix is multiplied by the scalar 2:
\[
\begin{bmatrix} 2x & -y \\ 3y & -4z \end{bmatrix}
\]
- The resulting matrix from these operations should equal the third matrix:
\[
\begin{bmatrix} 16 & (6 - y) \\ 20 & 16 \end{bmatrix}
\]
3. To solve this system, set up equations by comparing corresponding elements from the left and right matrices after performing matrix addition and scalar multiplication on the left-hand side expressions. Lookup each element and equate them individually to solve for \( x \), \( y \), and \( z \).
Solve each element in the matrix equation separately to find the values of \( x \), \( y \), and \( z \).](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F87020c12-9fad-41df-8977-4681e6b0c96c%2Fefddcb8f-31a1-4a76-85cf-d39538803970%2Fxsbs3e5o_processed.jpeg&w=3840&q=75)
Transcribed Image Text:Certainly! Below is a transcription of the image content suitable for an educational website:
---
**Solve for \( x \), \( y \), and \( z \).**
\[
4 \begin{bmatrix} x & y \\ y & z \end{bmatrix} + 2 \begin{bmatrix} 2x & -y \\ 3y & -4z \end{bmatrix} = \begin{bmatrix} 16 & (6 - y) \\ 20 & 16 \end{bmatrix}
\]
**Calculate:**
\[ x = \_\_\_\_ \]
\[ y = \_\_\_\_ \]
\[ z = \_\_\_\_ \]
---
**Explanation of the Equation:**
1. The problem is a system of matrix equations. It involves finding the variables \( x \), \( y \), and \( z \) that satisfy the given equality.
2. The equation consists of three matrices:
- The first matrix is multiplied by the scalar 4:
\[
\begin{bmatrix} x & y \\ y & z \end{bmatrix}
\]
- The second matrix is multiplied by the scalar 2:
\[
\begin{bmatrix} 2x & -y \\ 3y & -4z \end{bmatrix}
\]
- The resulting matrix from these operations should equal the third matrix:
\[
\begin{bmatrix} 16 & (6 - y) \\ 20 & 16 \end{bmatrix}
\]
3. To solve this system, set up equations by comparing corresponding elements from the left and right matrices after performing matrix addition and scalar multiplication on the left-hand side expressions. Lookup each element and equate them individually to solve for \( x \), \( y \), and \( z \).
Solve each element in the matrix equation separately to find the values of \( x \), \( y \), and \( z \).
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