Calculate the determinant of I = [[1, 2, 1], [0, 1, 2], [1, 0, 1]]. (2021)

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Q: Calculate the determinant of I = [[1, 2, 1], [0, 1, 2], [1, 0, 1]]. (2021)

Solution: Det(I) = 1(1*1 - 2*0) - 2(0*1 - 2*1) + 1(0*0 - 1*1) = 1(1) - 2(-2) + 1(-1) = 1 + 4 - 1 = 4.

Steps: 9

Step 1: Identify the matrix I = [[1, 2, 1], [0, 1, 2], [1, 0, 1]].
Step 2: Write down the formula for the determinant of a 3x3 matrix: Det(I) = 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 the matrix to the variables: a = 1, b = 2, c = 1, d = 0, e = 1, f = 2, g = 1, h = 0, i = 1.
Step 4: Calculate the first part: ei - fh = (1*1) - (2*0) = 1 - 0 = 1.
Step 5: Calculate the second part: di - fg = (0*1) - (2*1) = 0 - 2 = -2.
Step 6: Calculate the third part: dh - eg = (0*0) - (1*1) = 0 - 1 = -1.
Step 7: Substitute these values back into the determinant formula: Det(I) = 1(1) - 2(-2) + 1(-1).
Step 8: Simplify the expression: Det(I) = 1 + 4 - 1.
Step 9: Calculate the final result: Det(I) = 4.