What is the determinant of G = [[5, 4], [2, 3]]? (2020)

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Question: What is the determinant of G = [[5, 4], [2, 3]]? (2020)

Options:

Correct Answer: 10

Exam Year: 2020

Solution:

Det(G) = (5*3) - (4*2) = 15 - 8 = 7.

What is the determinant of G = [[5, 4], [2, 3]]? (2020)

What is the determinant of G = [[5, 4], [2, 3]]? (2020)

Step 1: Identify the elements of the matrix G. The matrix G is [[5, 4], [2, 3]].
Step 2: Label the elements of the matrix. Let a = 5, b = 4, c = 2, 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) = (5 * 3) - (4 * 2).
Step 5: Calculate the first part: 5 * 3 = 15.
Step 6: Calculate the second part: 4 * 2 = 8.
Step 7: Subtract the second part from the first part: 15 - 8 = 7.
Step 8: Conclude that the determinant of G is 7.

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