If I = [[1, 2, 3], [0, 1, 4], [5, 6, 0]], find the determinant of I.
Practice Questions
Q1
If I = [[1, 2, 3], [0, 1, 4], [5, 6, 0]], find the determinant of I.
-24
24
0
12
Questions & Step-by-Step Solutions
If I = [[1, 2, 3], [0, 1, 4], [5, 6, 0]], find the determinant of I.
Step 1: Identify the matrix I, which is [[1, 2, 3], [0, 1, 4], [5, 6, 0]].
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 the values from matrix I to the variables: a = 1, b = 2, c = 3, d = 0, e = 1, f = 4, g = 5, h = 6, i = 0.
Step 4: Calculate ei - fh: ei = 1*0 = 0 and fh = 4*6 = 24, so ei - fh = 0 - 24 = -24.
Step 5: Calculate di - fg: di = 0*0 = 0 and fg = 4*5 = 20, so di - fg = 0 - 20 = -20.
Step 7: Substitute these values into the determinant formula: det(I) = 1*(-24) - 2*(-20) + 3*(-5).
Step 8: Calculate each term: 1*(-24) = -24, -2*(-20) = 40, and 3*(-5) = -15.
Step 9: Combine the results: -24 + 40 - 15 = 1.
Step 10: The final result is det(I) = 1.
Determinant of a 3x3 Matrix – The determinant of a 3x3 matrix can be calculated using the formula: det(A) = a(ei - fh) - b(di - fg) + c(dh - eg), where A = [[a, b, c], [d, e, f], [g, h, i]].
Matrix Multiplication and Addition – Understanding how to perform multiplication and addition of matrix elements is crucial for calculating determinants.
