Determinant properties - ML & AI Coding

38. Determinant properties

medium

General

staff

You’ll practice core determinant properties that show up a lot in linear algebra interviews, like how row operations affect the determinant. Given a square matrix as a NumPy array, compute its determinant using only simple row operations and a recursive base case.

\det(A) = (-1)^k \prod_{i=1}^n U_{ii}

Requirements

Implement the function

python

Rules:

Use the determinant identity $\det(A)=\prod_{i=1}^{n} u_{ii} \cdot s$ where (u_{ii}) are diagonal entries after converting (A) to an upper-triangular matrix via row operations, and (s\in{+1,-1}) tracks row swaps.
Convert A to an upper-triangular form using only row swaps and “add multiple of row” operations (Gaussian elimination style).
Track row swaps to adjust the sign of the final determinant.
Do not call np.linalg.det (or any other prebuilt determinant routine).
Return a single float.

Example

python

Output:

python

Input Signature

Argument	Type
A	np.ndarray

Output Signature

Return Name	Type
value	float

Constraints

No np.linalg.det or determinant helpers
Use row swaps + row addition only
Return single float

Hint 1

Start by creating a float copy mat = A.astype(float).copy() and keep a sign variable initialized to +1.

Hint 2

Perform Gaussian elimination to make the matrix upper-triangular using only:

swap rows when the pivot is zero (flip sign),
add a multiple of the pivot row to rows below (does not change determinant).

Hint 3

Update rows with vectorization: mat[row, col:] -= factor * mat[col, col:]. Finally, det = sign * np.prod(np.diag(mat)).

Roles

ML Engineer

AI Engineer

Companies

General

Levels

staff

senior

Input Arguments

Edit values below to test with custom inputs

You need tolog in/sign upto run or submit