https://file.aiquickdraw.com/mathbot/file/1725940497722zypudtq4.jpg

The problem asks to find the rank of the matrix \( A \), which is given as:

\[
A = \begin{pmatrix} 1 & -3 & 4 & 7 \\ 9 & 1 & 2 & 0 \end{pmatrix}
\]

### Steps to Find the Rank:
1. **Row Reduction**: Convert the matrix into its row echelon form (REF) or reduced row echelon form (RREF) using elementary row operations.
2. **Identify Non-Zero Rows**: The rank of the matrix is the number of non-zero rows in its echelon form.

Let's proceed with the row reduction to find the rank.The rank of the matrix \( A \) is \( 2 \). 

This means that there are two linearly independent rows in the matrix, indicating that the matrix has a rank of 2.

Would you like further details on how the rank was determined, or do you have any other questions?

Here are five related questions you could explore:
1. What does it mean for a matrix to be full rank?
2. How do you find the rank of a larger matrix, such as a 3x4 matrix?
3. What is the relationship between rank and the number of linearly independent columns?
4. How does row reduction help in determining the rank?
5. How does the concept of rank relate to solving systems of linear equations?

**Tip:** When calculating the rank of a matrix, reducing the matrix to row echelon form can help visually identify the number of linearly independent rows.

Find the rank of the matrix A = \( \begin{pmatrix} 1 & -3 & 4 & 7 \\ 9 & 1 & 2 & 0 \end{pmatrix} \)

Learn how to find the rank of the matrix A = (1, -3, 4, 7; 9, 1, 2, 0) using row reduction techniques. This problem demonstrates key concepts in linear algebra, including matrix rank, elementary row operations, and linear independence.

Math Problem Statement

Solution

Ask a new question for Free

By Image

Math Problem Analysis

Mathematical Concepts

Formulas

Theorems

Suitable Grade Level

Related Recommendation