Question: What is the rank of the matrix [[1, 2, 3], [4, 5, 6], [7, 8, 9]]?
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Correct Answer: 2
Solution:
The rank of the matrix is 2, as the rows are linearly dependent.
What is the rank of the matrix [[1, 2, 3], [4, 5, 6], [7, 8, 9]]?
Practice Questions
Q1
What is the rank of the matrix [[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 [[1, 2, 3], [4, 5, 6], [7, 8, 9]]?
Correct Answer: 2
Step 1: Write down the matrix: [[1, 2, 3], [4, 5, 6], [7, 8, 9]].
Step 2: Identify the number of rows and columns in the matrix. This matrix 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). This means the rows are not independent.
Step 5: Since the rows are dependent, we can find the maximum number of independent rows. In this case, we can only have 2 independent rows.
Step 6: Therefore, the rank of the matrix is 2.
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