What is the determinant of G = [[1, 2, 3], [4, 5, 6], [7, 8, 9]]? (2020)
Practice Questions
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What is the determinant of G = [[1, 2, 3], [4, 5, 6], [7, 8, 9]]? (2020)
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Questions & Step-by-Step Solutions
What is the determinant of G = [[1, 2, 3], [4, 5, 6], [7, 8, 9]]? (2020)
Step 1: Identify the matrix G. G = [[1, 2, 3], [4, 5, 6], [7, 8, 9]].
Step 2: Write down the formula for the determinant of a 3x3 matrix: Det(G) = a(ei - fh) - b(di - fg) + c(dh - eg), where G = [[a, b, c], [d, e, f], [g, h, i]].
Step 3: Assign values from the matrix G to the variables: a = 1, b = 2, c = 3, d = 4, e = 5, f = 6, g = 7, h = 8, i = 9.
Step 4: Calculate the first part: ei - fh = 5*9 - 6*8 = 45 - 48 = -3.
Step 5: Calculate the second part: di - fg = 4*9 - 6*7 = 36 - 42 = -6.
Step 6: Calculate the third part: dh - eg = 4*8 - 5*7 = 32 - 35 = -3.
Step 7: Substitute these values back into the determinant formula: Det(G) = 1*(-3) - 2*(-6) + 3*(-3).
