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Calculate the determinant: | 2 3 1 | | 1 0 4 | | 0 5 2 |.
Calculate the determinant: | 2 3 1 | | 1 0 4 | | 0 5 2 |.
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Q1
Calculate the determinant: | 2 3 1 | | 1 0 4 | | 0 5 2 |.
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Using the determinant formula, we find that the determinant evaluates to 0.
Questions & Step-by-step Solutions
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Q: Calculate the determinant: | 2 3 1 | | 1 0 4 | | 0 5 2 |.
Solution:
Using the determinant formula, we find that the determinant evaluates to 0.
Steps: 9
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Step 1: Write down the matrix: | 2 3 1 | | 1 0 4 | | 0 5 2 |.
Step 2: Identify the elements of the matrix: a = 2, b = 3, c = 1, d = 1, e = 0, f = 4, g = 0, h = 5, i = 2.
Step 3: Use the determinant formula for a 3x3 matrix: det(A) = a(ei - fh) - b(di - fg) + c(dh - eg).
Step 4: Calculate ei - fh: (0*2) - (4*5) = 0 - 20 = -20.
Step 5: Calculate di - fg: (1*2) - (4*0) = 2 - 0 = 2.
Step 6: Calculate dh - eg: (1*5) - (0*0) = 5 - 0 = 5.
Step 7: Substitute these values into the determinant formula: det(A) = 2*(-20) - 3*(2) + 1*(5).
Step 8: Calculate: det(A) = -40 - 6 + 5 = -41.
Step 9: Since the determinant is not zero, the final answer is that the determinant evaluates to -41.
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