What is the determinant of G = [[3, 2], [1, 4]]? (2022)

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Question: What is the determinant of G = [[3, 2], [1, 4]]? (2022)

Options:

Correct Answer: 10

Exam Year: 2022

Solution:

The determinant of G is (3*4) - (2*1) = 12 - 2 = 10.

What is the determinant of G = [[3, 2], [1, 4]]? (2022)

What is the determinant of G = [[3, 2], [1, 4]]? (2022)

Step 1: Identify the matrix G, which is [[3, 2], [1, 4]].
Step 2: Recognize that the determinant of a 2x2 matrix [[a, b], [c, d]] is calculated using the formula (a*d) - (b*c).
Step 3: In our matrix G, a = 3, b = 2, c = 1, and d = 4.
Step 4: Substitute the values into the formula: (3*4) - (2*1).
Step 5: Calculate 3*4, which equals 12.
Step 6: Calculate 2*1, which equals 2.
Step 7: Subtract the second result from the first: 12 - 2.
Step 8: The final result is 10, which is the determinant of matrix G.

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