If H = [[1, 2, 3], [0, 1, 4], [5, 6, 0]], find the determinant of H. (2022)
Practice Questions
Q1
If H = [[1, 2, 3], [0, 1, 4], [5, 6, 0]], find the determinant of H. (2022)
-24
24
0
12
Questions & Step-by-Step Solutions
If H = [[1, 2, 3], [0, 1, 4], [5, 6, 0]], find the determinant of H. (2022)
Step 1: Identify the matrix H, which is H = [[1, 2, 3], [0, 1, 4], [5, 6, 0]].
Step 2: Write down the formula for the determinant of a 3x3 matrix: det(H) = 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 the values from matrix H to the variables: a = 1, b = 2, c = 3, d = 0, e = 1, f = 4, g = 5, h = 6, i = 0.
Step 4: Calculate ei - fh: ei = 1*0 = 0 and fh = 4*6 = 24, so ei - fh = 0 - 24 = -24.
Step 5: Calculate di - fg: di = 0*0 = 0 and fg = 4*5 = 20, so di - fg = 0 - 20 = -20.
