Find the RREF of the matrix

⎡⎣⎢⎢⎢⎢⎢⎢−2−2−232−421−4−422−1−2−1⎤⎦⎥⎥⎥⎥⎥⎥

The Reduced Row Echelon Form (RREF) of the given matrix is:

\[
\begin{bmatrix}
1 & 0 & 0 \\
0 & 1 & 0 \\
0 & 0 & 1 \\
0 & 0 & 0 \\
0 & 0 & 0
\end{bmatrix}
\]

This shows that the matrix has full rank (rank = 3), and the system of equations represented by this matrix has a unique solution.

Would you like more details or have any questions?

Here are five related questions for deeper exploration:
1. What is the significance of the rank of a matrix?
2. How does RREF relate to solving systems of linear equations?
3. Can a matrix always be reduced to RREF?
4. What are the conditions for a matrix to have a unique solution based on RREF?
5. How does RREF help in determining the linear independence of vectors?

**Tip:** The number of non-zero rows in the RREF of a matrix corresponds to the rank of the matrix.

Find the RREF of the matrix ⎡⎣⎢⎢⎢⎢⎢⎢−2−2−232−421−4−422−1−2−1⎤⎦⎥⎥⎥⎥⎥⎥

Discover how to compute the Reduced Row Echelon Form (RREF) of a matrix, including a detailed step-by-step solution. This problem highlights key linear algebra concepts such as matrix rank, row operations, and the relationship between RREF and solutions to linear systems. Suitable for undergraduate students studying Linear Algebra.

Math Problem Statement

Solution

Ask a new question for Free

By Image

Math Problem Analysis

Mathematical Concepts

Formulas

Theorems

Suitable Grade Level

Related Recommendation