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Evaluate the determinant | 1 1 1 | | 1 2 3 | | 1 3 6 |.
Evaluate the determinant | 1 1 1 | | 1 2 3 | | 1 3 6 |.
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Q1
Evaluate the determinant | 1 1 1 | | 1 2 3 | | 1 3 6 |.
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The rows are linearly dependent, hence the determinant is 0.
Questions & Step-by-step Solutions
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Q: Evaluate the determinant | 1 1 1 | | 1 2 3 | | 1 3 6 |.
Solution:
The rows are linearly dependent, hence the determinant is 0.
Steps: 5
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Step 1: Write down the matrix you want to evaluate the determinant for: | 1 1 1 | | 1 2 3 | | 1 3 6 |.
Step 2: Identify the rows of the matrix: Row 1 is (1, 1, 1), Row 2 is (1, 2, 3), and Row 3 is (1, 3, 6).
Step 3: Check if the rows are linearly dependent. This means that one row can be formed by a combination of the others.
Step 4: Notice that Row 1 can be expressed as a combination of Row 2 and Row 3. Specifically, Row 1 = Row 2 - Row 3 + 1.
Step 5: Since the rows are linearly dependent, the determinant of the matrix is 0.
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