If A is a 3x3 matrix, what is the maximum number of linearly independent rows it

₹0.0

Question: If A is a 3x3 matrix, what is the maximum number of linearly independent rows it can have? (2023)

Options:

Correct Answer: 3

Exam Year: 2023

Solution:

A 3x3 matrix can have a maximum of 3 linearly independent rows, but the answer options are incorrect. The correct answer is 3.

If A is a 3x3 matrix, what is the maximum number of linearly independent rows it can have? (2023)

If A is a 3x3 matrix, what is the maximum number of linearly independent rows it can have? (2023)

Step 1: Understand what a 3x3 matrix is. A 3x3 matrix has 3 rows and 3 columns.
Step 2: Know what 'linearly independent' means. Rows are linearly independent if no row can be made by combining other rows.
Step 3: Realize that in a 3x3 matrix, you can have at most 3 rows.
Step 4: Think about the maximum number of rows that can be linearly independent. Since there are 3 rows, the maximum number of linearly independent rows is 3.
Step 5: Conclude that the maximum number of linearly independent rows in a 3x3 matrix is 3.

Linear Independence – The concept of linear independence refers to a set of vectors (or rows in a matrix) being independent if no vector can be expressed as a linear combination of the others.
Matrix Rank – The rank of a matrix is the maximum number of linearly independent row or column vectors in the matrix, which for a 3x3 matrix can be at most 3.