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

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

Options:

Correct Answer: 2

Exam Year: 2021

Solution:

Det(G) = (2*2) - (1*1) = 4 - 1 = 3.

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

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

Step 1: Identify the matrix G, which is [[2, 1], [1, 2]].
Step 2: Write down the formula for the determinant of a 2x2 matrix, which is Det(G) = (a*d) - (b*c), where G = [[a, b], [c, d]].
Step 3: Assign the values from the matrix to the variables: a = 2, b = 1, c = 1, d = 2.
Step 4: Substitute the values into the determinant formula: Det(G) = (2*2) - (1*1).
Step 5: Calculate the first part: 2*2 = 4.
Step 6: Calculate the second part: 1*1 = 1.
Step 7: Subtract the second part from the first part: 4 - 1 = 3.
Step 8: Conclude that the determinant of G is 3.

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