Math Problem Statement

RREF

Find the Reduced Row Echelon Form (RREF) of the given matrix.

Solution

The image shows a matrix:

[123466789]\begin{bmatrix} 1 & 2 & 3 \\ 4 & 6 & 6 \\ 7 & 8 & 9 \end{bmatrix}

You have asked for the Reduced Row Echelon Form (RREF) of this matrix. I will compute its RREF step-by-step.The Reduced Row Echelon Form (RREF) of the given matrix is:

[100010001]\begin{bmatrix} 1 & 0 & 0 \\ 0 & 1 & 0 \\ 0 & 0 & 1 \end{bmatrix}

This is the identity matrix, indicating that the original matrix is invertible.

Do you want further details or have any specific questions about this calculation?

Related Questions

  1. What are the steps to calculate the RREF for a matrix?
  2. How can we determine if a matrix is invertible?
  3. What is the significance of the pivot columns in RREF?
  4. How does the RREF differ from the echelon form?
  5. How can we find the inverse of this matrix using the RREF?

Tip: The RREF form is unique for any given matrix, which makes it useful for solving linear systems and checking linear independence.

Ask a new question for Free

By Image

Drop file here or Click Here to upload

Math Problem Analysis

Mathematical Concepts

Matrix Algebra
Linear Systems
Gaussian Elimination

Formulas

Row operations in matrix manipulation
Reduced Row Echelon Form conditions

Theorems

Fundamental Theorem of Linear Algebra
Invertibility of a matrix
Uniqueness of RREF

Suitable Grade Level

College Level