I ++ y + 22 Z 1) Consider the system of linear equations 3x 11. If we are using Cramer's Rule, we will have our solution as -I +2y = 0 |D₂| I= Dz D y = Z= |D₂| D D Please write the matrices D, Dz, Dy, D₂ separately without calculating the determinants. That means what are the matrices D, D2, Dy, Dz?
I ++ y + 22 Z 1) Consider the system of linear equations 3x 11. If we are using Cramer's Rule, we will have our solution as -I +2y = 0 |D₂| I= Dz D y = Z= |D₂| D D Please write the matrices D, Dz, Dy, D₂ separately without calculating the determinants. That means what are the matrices D, D2, Dy, Dz?
Linear Algebra: A Modern Introduction
4th Edition
ISBN:9781285463247
Author:David Poole
Publisher:David Poole
Chapter2: Systems Of Linear Equations
Section2.4: Applications
Problem 16EQ
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![### System of Linear Equations and Partial Fraction Decomposition
---
#### 1) Consider the system of linear equations
\[
\begin{cases}
x - y + 2z = 0 \\
3x + z = 11 \\
-x + 2y = 0
\end{cases}
\]
If we are using Cramer's Rule, we will have our solution as
\[
x = \frac{|D_x|}{D}, \quad y = \frac{|D_y|}{D}, \quad z = \frac{|D_z|}{D}
\]
Please write the matrices \(D, D_x, D_y, D_z\) separately without calculating the determinants. That means what are the matrices \(D, D_x, D_y, D_z\)?
---
#### 2) We will practice on the form of partial fraction: write the form of the partial fraction decomposition of the function. Do not determine the numerical values of the coefficients.
1)
\[
\frac{-10x^2 + 27x - 14}{(x13)^2(x + 2)}
\]
2)
\[
\frac{3x^2 - 2x + 8}{x^3 - x^2 + 2x - 2}
\]
---
By following the given instructions, students can practice setting up the necessary matrices for solving system of linear equations using Cramer's Rule and writing the form of partial fractions for given rational expressions.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F6bca0f7c-4a69-4d44-a0fc-404c8d0c241c%2F6757f0f1-1ab0-4645-b492-12cd2fa7eedc%2Fi2a1or_processed.jpeg&w=3840&q=75)
Transcribed Image Text:### System of Linear Equations and Partial Fraction Decomposition
---
#### 1) Consider the system of linear equations
\[
\begin{cases}
x - y + 2z = 0 \\
3x + z = 11 \\
-x + 2y = 0
\end{cases}
\]
If we are using Cramer's Rule, we will have our solution as
\[
x = \frac{|D_x|}{D}, \quad y = \frac{|D_y|}{D}, \quad z = \frac{|D_z|}{D}
\]
Please write the matrices \(D, D_x, D_y, D_z\) separately without calculating the determinants. That means what are the matrices \(D, D_x, D_y, D_z\)?
---
#### 2) We will practice on the form of partial fraction: write the form of the partial fraction decomposition of the function. Do not determine the numerical values of the coefficients.
1)
\[
\frac{-10x^2 + 27x - 14}{(x13)^2(x + 2)}
\]
2)
\[
\frac{3x^2 - 2x + 8}{x^3 - x^2 + 2x - 2}
\]
---
By following the given instructions, students can practice setting up the necessary matrices for solving system of linear equations using Cramer's Rule and writing the form of partial fractions for given rational expressions.
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