If G = [[1, 1], [1, -1]], find det(G). (2022)

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Question: If G = [[1, 1], [1, -1]], find det(G). (2022)

Options:

Correct Answer: 1

Exam Year: 2022

Solution:

Determinant of G = (1*-1) - (1*1) = -1 - 1 = -2.

If G = [[1, 1], [1, -1]], find det(G). (2022)

If G = [[1, 1], [1, -1]], find det(G). (2022)

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

Determinant of a 2x2 Matrix – The determinant of a 2x2 matrix [[a, b], [c, d]] is calculated using the formula ad - bc.