Calculate the determinant of H = [[1, 2, 1], [0, 1, 3], [2, 1, 0]]. (2020)
Practice Questions
Q1
Calculate the determinant of H = [[1, 2, 1], [0, 1, 3], [2, 1, 0]]. (2020)
-5
5
0
10
Questions & Step-by-Step Solutions
Calculate the determinant of H = [[1, 2, 1], [0, 1, 3], [2, 1, 0]]. (2020)
Step 1: Write down the matrix H: [[1, 2, 1], [0, 1, 3], [2, 1, 0]].
Step 2: Identify the elements of the matrix for the determinant formula. The formula for a 3x3 matrix is: 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 values from the matrix to the variables: a = 1, b = 2, c = 1, d = 0, e = 1, f = 3, g = 2, h = 1, i = 0.
Step 4: Calculate the first part: ei - fh = (1*0) - (3*1) = 0 - 3 = -3.
Step 5: Calculate the second part: di - fg = (0*0) - (3*2) = 0 - 6 = -6.
Step 6: Calculate the third part: dh - eg = (0*1) - (1*2) = 0 - 2 = -2.
Step 7: Substitute these values back into the determinant formula: Det(H) = 1*(-3) - 2*(-6) + 1*(-2).
Step 9: Calculate the final result: -3 + 12 = 9, then 9 - 2 = 7.
Step 10: The determinant of matrix H is 7.
Determinant Calculation – The process of calculating the determinant of a 3x3 matrix using the formula involving minors and cofactors.
Matrix Operations – Understanding how to perform basic operations on matrices, including multiplication and addition, which are often involved in determinant calculations.
