Math Problem Statement

find rank using column echolon form

Find the rank using column echelon form for the given matrix.

Solution

The rank of the given matrix, determined using its column echelon form, is 2.

Would you like further details or have any questions?

Here are 5 related questions to expand on this topic:

  1. What is the definition of a matrix rank?
  2. How does column echelon form differ from row echelon form?
  3. Can the rank of a matrix change if a row is added or removed?
  4. What does the rank of a matrix tell us about the solution to a system of equations?
  5. How can we compute the rank of a matrix using determinant properties?

Tip: The rank of a matrix is the maximum number of linearly independent columns (or rows) it contains.

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Math Problem Analysis

Mathematical Concepts

Linear Algebra
Matrix Rank
Column Echelon Form

Formulas

Matrix rank is the maximum number of linearly independent columns in the matrix.

Theorems

Rank-Nullity Theorem
Echelon form theorems

Suitable Grade Level

College Level (Linear Algebra)