If H = [[1, 2, 1], [0, 1, 0], [2, 1, 1]], find det(H). (2021)
Practice Questions
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If H = [[1, 2, 1], [0, 1, 0], [2, 1, 1]], find det(H). (2021)
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Questions & Step-by-Step Solutions
If H = [[1, 2, 1], [0, 1, 0], [2, 1, 1]], find det(H). (2021)
Step 1: Identify the matrix H. H = [[1, 2, 1], [0, 1, 0], [2, 1, 1]].
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 H = [[a, b, c], [d, e, f], [g, h, i]].
Step 3: Assign values from matrix H to the variables: a = 1, b = 2, c = 1, d = 0, e = 1, f = 0, g = 2, h = 1, i = 1.
Step 4: Calculate ei - fh: ei = 1*1 = 1 and fh = 0*1 = 0, so ei - fh = 1 - 0 = 1.
Step 5: Calculate di - fg: di = 0*1 = 0 and fg = 0*2 = 0, so di - fg = 0 - 0 = 0.
