Calculate the determinant of H = [[1, 2, 3], [0, 1, 4], [5, 6, 0]]. (2021)
Practice Questions
Q1
Calculate the determinant of H = [[1, 2, 3], [0, 1, 4], [5, 6, 0]]. (2021)
-14
14
0
10
Questions & Step-by-Step Solutions
Calculate the determinant of H = [[1, 2, 3], [0, 1, 4], [5, 6, 0]]. (2021)
Step 1: Write down the matrix H: [[1, 2, 3], [0, 1, 4], [5, 6, 0]].
Step 2: Identify the elements of the first row: a = 1, b = 2, c = 3.
Step 3: Calculate the determinant using the formula: Det(H) = a * Det(M1) - b * Det(M2) + c * Det(M3), where M1, M2, and M3 are the 2x2 matrices obtained by removing the row and column of each element.
Step 4: Calculate M1 by removing the first row and first column: M1 = [[1, 4], [6, 0]].
Step 5: Calculate the determinant of M1: Det(M1) = (1*0) - (4*6) = 0 - 24 = -24.
Step 6: Calculate M2 by removing the first row and second column: M2 = [[0, 4], [5, 0]].
Step 7: Calculate the determinant of M2: Det(M2) = (0*0) - (4*5) = 0 - 20 = -20.
Step 8: Calculate M3 by removing the first row and third column: M3 = [[0, 1], [5, 6]].
Step 9: Calculate the determinant of M3: Det(M3) = (0*6) - (1*5) = 0 - 5 = -5.
Step 10: Substitute the determinants back into the formula: Det(H) = 1*(-24) - 2*(-20) + 3*(-5).
Step 13: Final calculation: -24 + 40 = 16, then 16 - 15 = 1.
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.
