What is det(M) for M = [ [2, 1], [5, 3] ]?

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Multiple Choice

What is det(M) for M = [ [2, 1], [5, 3] ]?

Explanation:
The determinant of a 2×2 matrix [ [a, b], [c, d] ] is ad − bc. For this matrix, a = 2, b = 1, c = 5, d = 3. Compute ad = 2×3 = 6 and bc = 1×5 = 5, then det(M) = 6 − 5 = 1. So the determinant is 1. This positive value indicates the linear transformation preserves orientation and scales areas by a factor of 1.

The determinant of a 2×2 matrix [ [a, b], [c, d] ] is ad − bc. For this matrix, a = 2, b = 1, c = 5, d = 3. Compute ad = 2×3 = 6 and bc = 1×5 = 5, then det(M) = 6 − 5 = 1. So the determinant is 1. This positive value indicates the linear transformation preserves orientation and scales areas by a factor of 1.

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