Question: What is the rank of the matrix A = [[1, 2, 3], [4, 5, 6], [7, 8, 9]]?
Options:
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Correct Answer: 2
Solution:
The rows of A are linearly dependent, hence the rank is 2.
What is the rank of the matrix A = [[1, 2, 3], [4, 5, 6], [7, 8, 9]]?
Practice Questions
Q1
What is the rank of the matrix A = [[1, 2, 3], [4, 5, 6], [7, 8, 9]]?
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Questions & Step-by-Step Solutions
What is the rank of the matrix A = [[1, 2, 3], [4, 5, 6], [7, 8, 9]]?
Step 1: Understand what the rank of a matrix is. The rank is the maximum number of linearly independent rows or columns in the matrix.
Step 2: Look at the matrix A = [[1, 2, 3], [4, 5, 6], [7, 8, 9]]. It has 3 rows and 3 columns.
Step 3: Check if the rows are linearly independent. This means we need to see if one row can be formed by a combination of the others.
Step 4: Notice that the third row (7, 8, 9) can be formed by adding the first row (1, 2, 3) and the second row (4, 5, 6) together. This means the rows are dependent.
Step 5: Since the rows are dependent, we can only have 2 linearly independent rows.
Step 6: Therefore, the rank of the matrix A is 2.
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