Calculate the determinant of D = [[4, 5, 6], [7, 8, 9], [1, 2, 3]]. (2020)
Practice Questions
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Calculate the determinant of D = [[4, 5, 6], [7, 8, 9], [1, 2, 3]]. (2020)
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Determinant of D = 4(8*3 - 9*2) - 5(7*3 - 9*1) + 6(7*2 - 8*1) = 0.
Questions & Step-by-step Solutions
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Q
Q: Calculate the determinant of D = [[4, 5, 6], [7, 8, 9], [1, 2, 3]]. (2020)
Solution: Determinant of D = 4(8*3 - 9*2) - 5(7*3 - 9*1) + 6(7*2 - 8*1) = 0.
Steps: 10
Step 1: Identify the matrix D, which is D = [[4, 5, 6], [7, 8, 9], [1, 2, 3]].
Step 2: Use the formula for the determinant of a 3x3 matrix: det(D) = a(ei - fh) - b(di - fg) + c(dh - eg), where the matrix is [[a, b, c], [d, e, f], [g, h, i]].
Step 3: Assign values from the matrix to the variables: a = 4, b = 5, c = 6, d = 7, e = 8, f = 9, g = 1, h = 2, i = 3.
Step 4: Calculate ei - fh: ei = 8*3 = 24 and fh = 9*2 = 18, so ei - fh = 24 - 18 = 6.
Step 5: Calculate di - fg: di = 7*3 = 21 and fg = 9*1 = 9, so di - fg = 21 - 9 = 12.
