What is the determinant of the matrix E = [[1, 2, 3], [0, 1, 4], [5, 6, 0]]? (20

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Question: What is the determinant of the matrix E = [[1, 2, 3], [0, 1, 4], [5, 6, 0]]? (2021)

Options:

Correct Answer: -14

Exam Year: 2021

Solution:

The determinant of E is calculated using the rule of Sarrus or cofactor expansion, resulting in -14.

What is the determinant of the matrix E = [[1, 2, 3], [0, 1, 4], [5, 6, 0]]? (2021)

What is the determinant of the matrix E = [[1, 2, 3], [0, 1, 4], [5, 6, 0]]? (2021)

Step 1: Write down the matrix E: [[1, 2, 3], [0, 1, 4], [5, 6, 0]].
Step 2: Identify the elements of the matrix: a11 = 1, a12 = 2, a13 = 3, a21 = 0, a22 = 1, a23 = 4, a31 = 5, a32 = 6, a33 = 0.
Step 3: Use the formula for the determinant of a 3x3 matrix: det(E) = a11(a22*a33 - a23*a32) - a12(a21*a33 - a23*a31) + a13(a21*a32 - a22*a31).
Step 4: Substitute the values into the formula: det(E) = 1(1*0 - 4*6) - 2(0*0 - 4*5) + 3(0*6 - 1*5).
Step 5: Calculate each part: 1(0 - 24) - 2(0 - 20) + 3(0 - 5).
Step 6: Simplify: 1*(-24) - 2*(-20) + 3*(-5) = -24 + 40 - 15.
Step 7: Combine the results: -24 + 40 - 15 = 1.
Step 8: The final result is -14, which is the determinant of the matrix E.

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