**3. Find the solution set of the following vector equation.**\[x_1 \begin{pmatrix}-2 \\3 \\-3 \end{pmatrix} +x_2 \begin{pmatrix}6 \\-9 \\9 \end{pmatrix}+x_3\begin{pmatrix}-6 \\9 \\-9 \end{pmatrix} +x_4\begin{pmatrix}-2 \\1 \\-2 \end{pmatrix}=\begin{pmatrix}4 \\0 \\3 \end{pmatrix}\]In this equation, we are given a combination of vector coefficients multiplied by variables $(x_1, x_2, x_3, x_4)$ summing up to a result vector on the right-hand side. The goal is to find out the values of $x_1, x_2, x_3,$ and $x_4$ that satisfy the vector equation.**Explanation of Vectors:**1. The first vector is scaled by $x_1$: $ \begin{pmatrix} -2 \\ 3 \\ -3 \end{pmatrix} $2. The second vector is scaled by $x_2$: $ \begin{pmatrix} 6 \\ -9 \\ 9 \end{pmatrix} $3. The third vector is scaled by $x_3$: $ \begin{pmatrix} -6 \\ 9 \\ -9 \end{pmatrix} $4. The fourth vector is scaled by $x_4$: $ \begin{pmatrix} -2 \\ 1 \\ -2 \end{pmatrix} $The combination of these vectors, across the respective $x$ coefficients, should be equal to the vector on the right-hand side:$\begin{pmatrix}4 \\0 \\3 \end{pmatrix}$**Approach for Solving:**To solve this, you will need to set up a system

In this question, we solve the system of equations. Here, we write the system in the matrix form,…

Answered: Find the solution set of the following…

Math

Advanced Math

Find the solution set of the following vector equation.

Algebra & Trigonometry with Analytic Geometry

13th Edition

ISBN:9781133382119

Author:Swokowski

Publisher:Swokowski

Chapter3: Functions And Graphs

Section3.3: Lines

Problem 27E

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Concept explainers

Linear Algebra

In mathematics, problems can be solved by the arithmetic operators like addition, subtraction, multiplication, and division. In algebra, we represent the numbers by any letter called a variable. If these variables are of degree 1, then it is studied under linear algebra. The first-degree equations involving algebraic expressions are called linear equations. That is, if you represent it by drawing a graph you will get a straight line.

Question

**3. Find the solution set of the following vector equation.**

\[
x_1
\begin{pmatrix}
-2 \\
3 \\
-3
\end{pmatrix}
+
x_2
\begin{pmatrix}
6 \\
-9 \\
9
\end{pmatrix}
+
x_3
\begin{pmatrix}
-6 \\
9 \\
-9
\end{pmatrix}
+
x_4
\begin{pmatrix}
-2 \\
1 \\
-2
\end{pmatrix}
=
\begin{pmatrix}
4 \\
0 \\
3
\end{pmatrix}
\]

In this equation, we are given a combination of vector coefficients multiplied by variables $(x_1, x_2, x_3, x_4)$ summing up to a result vector on the right-hand side. The goal is to find out the values of $x_1, x_2, x_3,$ and $x_4$ that satisfy the vector equation.

**Explanation of Vectors:**

1. The first vector is scaled by $x_1$:
$
\begin{pmatrix}
-2 \\
3 \\
-3
\end{pmatrix}
$

2. The second vector is scaled by $x_2$:
$
\begin{pmatrix}
6 \\
-9 \\
9
\end{pmatrix}
$

3. The third vector is scaled by $x_3$:
$
\begin{pmatrix}
-6 \\
9 \\
-9
\end{pmatrix}
$

4. The fourth vector is scaled by $x_4$:
$
\begin{pmatrix}
-2 \\
1 \\
-2
\end{pmatrix}
$

The combination of these vectors, across the respective $x$ coefficients, should be equal to the vector on the right-hand side:
$
\begin{pmatrix}
4 \\
0 \\
3
\end{pmatrix}
$

**Approach for Solving:**

To solve this, you will need to set up a system

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