write the matrix set up $$ {\displaylines\sum3x+2y-z=9\\ x-y+3z=3_{}\\ 2x+3y-4z=6} $$

To set up the system of equations into matrix form, we follow these steps:

Given the system of equations:

\[
\begin{aligned}
1) \quad 3x + 2y - z &= 9 \\
2) \quad x - y + 3z &= 3 \\
3) \quad 2x + 3y - 4z &= 6 \\
\end{aligned}
\]

### Step 1: Write the coefficient matrix (A)
The coefficient matrix consists of the coefficients of the variables $x$, $y$, and $z$ from the system of equations:

\[
A = \begin{pmatrix}
3 & 2 & -1 \\
1 & -1 & 3 \\
2 & 3 & -4
\end{pmatrix}
\]

### Step 2: Write the variable matrix (X)
This matrix contains the variables $x$, $y$, and $z$:

\[
X = \begin{pmatrix}
x \\
y \\
z
\end{pmatrix}
\]

### Step 3: Write the constant matrix (B)
The constants on the right-hand side of the equations form the constant matrix:

\[
B = \begin{pmatrix}
9 \\
3 \\
6
\end{pmatrix}
\]

### Step 4: Matrix equation form
Now, we can write the system of equations as a matrix equation in the form $AX = B$:

\[
\begin{pmatrix}
3 & 2 & -1 \\
1 & -1 & 3 \\
2 & 3 & -4
\end{pmatrix}
\begin{pmatrix}
x \\
y \\
z
\end{pmatrix}
=
\begin{pmatrix}
9 \\
3 \\
6
\end{pmatrix}
\]

This is the matrix setup for the given system of equations.

---

Would you like further details or have any questions?  
Here are 5 related questions to consider:

1. How can we solve this system using matrix operations?
2. What are the different methods to solve a system of linear equations?
3. What is the determinant of the coefficient matrix?
4. Can this system of equations be solved using Cramer's Rule?
5. How would you use Gaussian elimination to solve this system?

**Tip:** When solving systems of linear equations, always check if the coefficient matrix is invertible to ensure a unique solution exists!

Learn how to set up a system of linear equations into matrix form with a detailed step-by-step solution. This problem involves writing the coefficient matrix, variable matrix, and constant matrix. Suitable for high school students in Grades 10-12.

Math Problem Statement

Solution

Ask a new question for Free

By Image

Math Problem Analysis

Mathematical Concepts

Formulas

Theorems

Suitable Grade Level

Related Recommendation