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Calculate the determinant: | 2 3 1 | | 1 0 2 | | 0 1 3 |.
Calculate the determinant: | 2 3 1 | | 1 0 2 | | 0 1 3 |.
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Calculate the determinant: | 2 3 1 | | 1 0 2 | | 0 1 3 |.
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The determinant evaluates to 0 as the rows are linearly dependent.
Questions & Step-by-step Solutions
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Q: Calculate the determinant: | 2 3 1 | | 1 0 2 | | 0 1 3 |.
Solution:
The determinant evaluates to 0 as the rows are linearly dependent.
Steps: 5
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Step 1: Write down the matrix: | 2 3 1 | | 1 0 2 | | 0 1 3 |.
Step 2: Identify the rows of the matrix: Row 1 = [2, 3, 1], Row 2 = [1, 0, 2], Row 3 = [0, 1, 3].
Step 3: Check if the rows are linearly dependent. This means we need to see if one row can be made by combining the others.
Step 4: Notice that Row 3 can be formed by combining Row 1 and Row 2. Specifically, Row 3 = Row 1 - 2 * Row 2.
Step 5: Since the rows are linearly dependent, the determinant of the matrix is 0.
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