H13-311_V3.5 · Question #253
The determinant of square matrix A is a scalar.
The correct answer is A. True. A is correct because the determinant is a function that maps a square matrix to a single real (or complex) number - a scalar. For a 2×2 matrix [[a,b],[c,d]], det(A) = ad − bc, which yields one number, not a vector or matrix. B is wrong because there is no alternative output…
Question
The determinant of square matrix A is a scalar.
Options
- ATrue
- BFalse
How the community answered
(32 responses)- A81% (26)
- B19% (6)
Explanation
A is correct because the determinant is a function that maps a square matrix to a single real (or complex) number - a scalar. For a 2×2 matrix [[a,b],[c,d]], det(A) = ad − bc, which yields one number, not a vector or matrix.
B is wrong because there is no alternative output type for a determinant. It cannot be a matrix, vector, or undefined for a valid square matrix - it always resolves to a scalar value.
Memory tip: Think of "det" as a compression machine - it takes an entire square matrix and squishes it down to a single number that encodes geometric information (like how much the matrix scales area/volume). One matrix in, one scalar out.
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