Why does $\det(A) = 0$ imply linear dependence?
126769
Linear independence of columns implies non-zero determinant
122562
Cross product term in linear regression why is it zero
23615
Why does zero derivative imply a function is locally constant?
84341
Can the determinant of a matrix can be made $0$?
56102
Prove that there is no non-zero linear operator on $\mathbb C^{2}$ such that $(\alpha | T\alpha) = 0$
68973
Is the determinant differentiable?
66500
Proving that orthogonal vectors are linearly independent
101631
Determinant of a finite-dimensional matrix in terms of trace
94077
Proof of linear independence of $e^{at}$
11557
How to prove $\det(e^A) = e^{\operatorname{tr}(A)}$?
75002
show that $\det(A)=0$ in this case
57626
Are Jordan chains always linearly independent?
45261
Why is the determinant of a rotation matrix equal to 1?
152147
Why is a set of orthonormal vectors linearly independent?
106398
If $A$ is invertible show that $\det(A) \neq 0$
120407
Is every noninvertible matrix a zero divisor?
84522
A better proof for $\det(P) = \pm1$ if $P$ is an orthogonal matrix