What is the rank of the matrix B = [[1, 2, 3], [4, 5, 6], [7, 8, 9]]? (2019)
Practice Questions
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What is the rank of the matrix B = [[1, 2, 3], [4, 5, 6], [7, 8, 9]]? (2019)
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Questions & Step-by-Step Solutions
What is the rank of the matrix B = [[1, 2, 3], [4, 5, 6], [7, 8, 9]]? (2019)
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 B = [[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 that no row can be formed by a combination of the other rows.
Step 4: Notice that if you take the first row (1, 2, 3) and the second row (4, 5, 6), you can see that the third row (7, 8, 9) can be formed by adding the first two rows together. This means the rows are dependent.
Step 5: Since the rows are dependent, we can only count 2 of them as independent. Therefore, the rank of the matrix B is 2.
