What is the rank of the matrix D = [[1, 2, 3], [4, 5, 6], [7, 8, 9]]? (2019)
Practice Questions
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What is the rank of the matrix D = [[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 D = [[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 D = [[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 find a relationship with the third row (7, 8, 9).
Step 5: Specifically, if you add the first row and the second row, you get (5, 7, 9), which is not equal to the third row, but you can see that the rows are not independent.
Step 6: To confirm, you can perform row operations or calculate the determinant of the matrix. The determinant is 0, indicating that the rows are dependent.
Step 7: Since there are 3 rows but they are dependent, the maximum number of independent rows is 2.
