Math Problem Statement

Find the rank of the matrix A = [[2, 3, -2, 4], [3, -2, 1, 2], [3, 2, 3, 4], [-2, 4, 0, 5]]

Solution

The rank of the matrix AA is 4. This means all four rows (or columns) of the matrix are linearly independent.

Would you like more details on how the rank is determined or any other aspect of this solution?

Here are five related questions:

  1. What is the definition of the rank of a matrix?
  2. How can we use row-reduction to find the rank of a matrix?
  3. What is the significance of a matrix having full rank?
  4. How does the rank relate to the solutions of a system of linear equations?
  5. Can the rank of a matrix change when it is multiplied by another matrix?

Tip: The rank of a matrix is always less than or equal to the smallest dimension of the matrix.

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Math Problem Analysis

Mathematical Concepts

Linear Algebra
Matrices
Rank of a Matrix

Formulas

Rank of a Matrix
Gaussian Elimination or Row Reduction

Theorems

Rank-Nullity Theorem

Suitable Grade Level

Undergraduate (First Year - Linear Algebra)

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