What is the determinant of the matrix G = [[2, 4], [1, 3]]? (2021)

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

Options:

Correct Answer: 2

Exam Year: 2021

Solution:

The determinant of G is (2*3) - (4*1) = 6 - 4 = 2.

What is the determinant of the matrix G = [[2, 4], [1, 3]]? (2021)

What is the determinant of the matrix G = [[2, 4], [1, 3]]? (2021)

Step 1: Identify the elements of the matrix G. The matrix G is [[2, 4], [1, 3]].
Step 2: Label the elements of the matrix. Let a = 2, b = 4, c = 1, d = 3.
Step 3: Use the formula for the determinant of a 2x2 matrix, which is det(G) = (a * d) - (b * c).
Step 4: Substitute the values into the formula: det(G) = (2 * 3) - (4 * 1).
Step 5: Calculate the first part: 2 * 3 = 6.
Step 6: Calculate the second part: 4 * 1 = 4.
Step 7: Subtract the second part from the first part: 6 - 4 = 2.
Step 8: Conclude that the determinant of the matrix G is 2.

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