What is the determinant of the matrix E = [[1, 2, 3], [4, 5, 6], [7, 8, 9]]?
Practice Questions
1 question
Q1
What is the determinant of the matrix E = [[1, 2, 3], [4, 5, 6], [7, 8, 9]]?
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The determinant of E is 0 because the rows are linearly dependent.
Questions & Step-by-step Solutions
1 item
Q
Q: What is the determinant of the matrix E = [[1, 2, 3], [4, 5, 6], [7, 8, 9]]?
Solution: The determinant of E is 0 because the rows are linearly dependent.
Steps: 8
Step 1: Identify the matrix E, which is E = [[1, 2, 3], [4, 5, 6], [7, 8, 9]].
Step 2: Understand that the determinant is a special number that can be calculated from a square matrix.
Step 3: To find the determinant of a 3x3 matrix, use the formula: det(E) = a(ei - fh) - b(di - fg) + c(dh - eg), where the matrix is represented as [[a, b, c], [d, e, f], [g, h, i]].
Step 4: For matrix E, assign values: a=1, b=2, c=3, d=4, e=5, f=6, g=7, h=8, i=9.
Step 5: Calculate the parts of the formula: ei - fh = 5*9 - 6*8 = 45 - 48 = -3, di - fg = 4*9 - 6*7 = 36 - 42 = -6, dh - eg = 4*8 - 5*7 = 32 - 35 = -3.
Step 6: Substitute these values into the determinant formula: det(E) = 1*(-3) - 2*(-6) + 3*(-3).
Step 7: Calculate: det(E) = -3 + 12 - 9 = 0.
Step 8: Conclude that the determinant of matrix E is 0.
