What is the determinant of G = [[1, 1, 1], [1, 2, 3], [1, 3, 6]]? (2023)
Practice Questions
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What is the determinant of G = [[1, 1, 1], [1, 2, 3], [1, 3, 6]]? (2023)
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Questions & Step-by-Step Solutions
What is the determinant of G = [[1, 1, 1], [1, 2, 3], [1, 3, 6]]? (2023)
Step 1: Identify the matrix G. G = [[1, 1, 1], [1, 2, 3], [1, 3, 6]].
Step 2: Write down the formula for the determinant of a 3x3 matrix. For a matrix [[a, b, c], [d, e, f], [g, h, i]], the determinant is Det = a(ei - fh) - b(di - fg) + c(dh - eg).
Step 3: Assign values from matrix G to the formula. Here, a = 1, b = 1, c = 1, d = 1, e = 2, f = 3, g = 1, h = 3, i = 6.
Step 4: Calculate the first part: ei - fh = 2*6 - 3*3 = 12 - 9 = 3.
Step 5: Calculate the second part: di - fg = 1*6 - 1*3 = 6 - 3 = 3.
Step 6: Calculate the third part: dh - eg = 1*3 - 1*2 = 3 - 2 = 1.
Step 7: Substitute these values back into the determinant formula: Det(G) = 1(3) - 1(3) + 1(1).
