Question 1

What is a determinant?

Accepted Answer

A determinant is a scalar value defined for square matrices. It indicates whether the matrix has an inverse (non-zero determinant). Geometrically, it represents the scaling factor of the transformation.

Question 2

What is an inverse matrix?

Accepted Answer

An inverse matrix A^-1 satisfies A*A^-1 = I (identity matrix). It exists only when the determinant is non-zero. Singular matrices (det=0) have no inverse.

Question 3

What are eigenvalues?

Accepted Answer

Eigenvalues are scalars lambda satisfying Ax = lambda*x. They are found by solving det(A - lambda*I) = 0 and are fundamental in data analysis, physics, and engineering.

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