If C = [[1, 0, 2], [-1, 3, 1], [2, 1, 0]], find det(C).
Practice Questions
Q1
If C = [[1, 0, 2], [-1, 3, 1], [2, 1, 0]], find det(C).
-9
9
0
6
Questions & Step-by-Step Solutions
If C = [[1, 0, 2], [-1, 3, 1], [2, 1, 0]], find det(C).
Step 1: Identify the matrix C, which is C = [[1, 0, 2], [-1, 3, 1], [2, 1, 0]].
Step 2: Write down the formula for the determinant of a 3x3 matrix: det(C) = 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 matrix C to the variables: a = 1, b = 0, c = 2, d = -1, e = 3, f = 1, g = 2, h = 1, i = 0.
Step 4: Calculate the first part: ei - fh = (3*0) - (1*1) = 0 - 1 = -1.
Step 5: Calculate the second part: di - fg = (-1*0) - (1*2) = 0 - 2 = -2.
Step 6: Calculate the third part: dh - eg = (-1*1) - (3*2) = -1 - 6 = -7.
Step 7: Substitute these values back into the determinant formula: det(C) = 1*(-1) - 0 + 2*(-7).
Determinant of a 3x3 Matrix – The determinant of a 3x3 matrix can be calculated using the formula: det(A) = a(ei - fh) - b(di - fg) + c(dh - eg), where the matrix is represented as A = [[a, b, c], [d, e, f], [g, h, i]].
