Calculate the determinant of H = [[1, 2, 1], [0, 1, 2], [1, 0, 1]]. (2020)
Practice Questions
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Calculate the determinant of H = [[1, 2, 1], [0, 1, 2], [1, 0, 1]]. (2020)
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Questions & Step-by-Step Solutions
Calculate the determinant of H = [[1, 2, 1], [0, 1, 2], [1, 0, 1]]. (2020)
Step 1: Write down the matrix H: [[1, 2, 1], [0, 1, 2], [1, 0, 1]].
Step 2: Identify the elements of the matrix for the determinant formula. The matrix is a 3x3 matrix, so we will use the formula for the determinant of a 3x3 matrix.
Step 3: The formula for the determinant of 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 4: Assign the values from the matrix H to the variables: a = 1, b = 2, c = 1, d = 0, e = 1, f = 2, g = 1, h = 0, i = 1.
Step 5: Substitute the values into the determinant formula: Det(H) = 1(1*1 - 2*0) - 2(0*1 - 2*1) + 1(0*0 - 1*1).
Step 6: Calculate each part of the formula: 1(1*1 - 2*0) = 1(1 - 0) = 1(1) = 1.
Step 7: Calculate the second part: -2(0*1 - 2*1) = -2(0 - 2) = -2(-2) = 4.
Step 8: Calculate the third part: 1(0*0 - 1*1) = 1(0 - 1) = 1(-1) = -1.
Step 9: Combine all the results: Det(H) = 1 + 4 - 1.
Step 10: Final calculation: 1 + 4 - 1 = 4.
Determinant Calculation – The process of calculating the determinant of a 3x3 matrix using the formula involving minors and cofactors.
Matrix Properties – Understanding the properties of determinants, such as linearity and how row operations affect the determinant.
