Sent by you:

Solve the system of linear homogeneous equations : x1+x2+x3+x4=0 x1+3x2+2x3+4x4=0 2x1+x3-x4=0

We are given a system of linear homogeneous equations:

\[
\begin{aligned}
x_1 + x_2 + x_3 + x_4 &= 0 \\
x_1 + 3x_2 + 2x_3 + 4x_4 &= 0 \\
2x_1 + x_3 - x_4 &= 0
\end{aligned}
\]

### Step 1: Set up the augmented matrix
We can express the system as an augmented matrix (without the right-hand side since it’s homogeneous):

\[
\begin{pmatrix}
1 & 1 & 1 & 1 \\
1 & 3 & 2 & 4 \\
2 & 0 & 1 & -1


Solve the system of linear homogeneous equations: x1 + x2 + x3 + x4 = 0, x1 + 3x2 + 2x3 + 4x4 = 0, 2x1 + x3 - x4 = 0.

Explore how to solve the system of linear homogeneous equations x1 + x2 + x3 + x4 = 0, x1 + 3x2 + 2x3 + 4x4 = 0, and 2x1 + x3 - x4 = 0 using matrix methods and Gaussian elimination. This problem covers key linear algebra concepts like matrix operations and homogeneous system solutions, ideal for 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