Solve for x, and x2. 4 5 X1 19 3 2 X2 9 (Simplify your answers. Type integers or fractions.)
Solve for x, and x2. 4 5 X1 19 3 2 X2 9 (Simplify your answers. Type integers or fractions.)
Linear Algebra: A Modern Introduction
4th Edition
ISBN:9781285463247
Author:David Poole
Publisher:David Poole
Chapter3: Matrices
Section3.1: Matrix Operations
Problem 20EQ: Referring to Exercise 19, suppose that the unit cost of distributing the products to stores is the...
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Question
![**Solving Systems of Linear Equations Using Matrices**
In this exercise, we are given a system of linear equations represented in matrix form. Your task is to solve for the variables \(x_1\) and \(x_2\).
The matrix equation given is:
\[
\begin{pmatrix}
4 & 5 \\
3 & 2
\end{pmatrix}
\begin{pmatrix}
x_1 \\
x_2
\end{pmatrix}
=
\begin{pmatrix}
19 \\
9
\end{pmatrix}
\]
### Explanation:
1. The left matrix \(
\begin{pmatrix}
4 & 5 \\
3 & 2
\end{pmatrix}
\) represents the coefficients of the variables \(x_1\) and \(x_2\).
2. The middle matrix \(
\begin{pmatrix}
x_1 \\
x_2
\end{pmatrix}
\) represents the unknown variables we need to solve for.
3. The right matrix \(
\begin{pmatrix}
19 \\
9
\end{pmatrix}
\) represents the constants from the right-hand side of each equation.
To solve the equation, follow these steps:
- You can use matrix inversion, Gaussian elimination, or other methods for solving linear systems.
### Steps to Solve:
1. Write down the system of equations from the matrix representation:
\[
4x_1 + 5x_2 = 19
\]
\[
3x_1 + 2x_2 = 9
\]
2. Use an appropriate method to solve for the variables \(x_1\) and \(x_2\).
3. Simplify your answers and write them in integer or fraction form as required.
The answer format is:
\[
x_1 = \boxed{}
\]
\[
x_2 = \boxed{}
\]
(Simplify your answers. Type integers or fractions.)](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Ff60bf7ae-3e0a-47f1-9493-b686204b7388%2F812879f7-a2c0-4b25-bb97-33ba9bcc8ac9%2Fp6df62b_processed.jpeg&w=3840&q=75)
Transcribed Image Text:**Solving Systems of Linear Equations Using Matrices**
In this exercise, we are given a system of linear equations represented in matrix form. Your task is to solve for the variables \(x_1\) and \(x_2\).
The matrix equation given is:
\[
\begin{pmatrix}
4 & 5 \\
3 & 2
\end{pmatrix}
\begin{pmatrix}
x_1 \\
x_2
\end{pmatrix}
=
\begin{pmatrix}
19 \\
9
\end{pmatrix}
\]
### Explanation:
1. The left matrix \(
\begin{pmatrix}
4 & 5 \\
3 & 2
\end{pmatrix}
\) represents the coefficients of the variables \(x_1\) and \(x_2\).
2. The middle matrix \(
\begin{pmatrix}
x_1 \\
x_2
\end{pmatrix}
\) represents the unknown variables we need to solve for.
3. The right matrix \(
\begin{pmatrix}
19 \\
9
\end{pmatrix}
\) represents the constants from the right-hand side of each equation.
To solve the equation, follow these steps:
- You can use matrix inversion, Gaussian elimination, or other methods for solving linear systems.
### Steps to Solve:
1. Write down the system of equations from the matrix representation:
\[
4x_1 + 5x_2 = 19
\]
\[
3x_1 + 2x_2 = 9
\]
2. Use an appropriate method to solve for the variables \(x_1\) and \(x_2\).
3. Simplify your answers and write them in integer or fraction form as required.
The answer format is:
\[
x_1 = \boxed{}
\]
\[
x_2 = \boxed{}
\]
(Simplify your answers. Type integers or fractions.)
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