True of False: Every 3-dimensional subspace of $ \Bbb R^{2 \times 2}$ contains at least one invertible matrix.
2109
Max dimension of a subspace of singular $n\times n$ matrices
58774
There exist an infinite subset $S\subseteq\mathbb{R}^3$ such that any three vectors in $S$ are linearly independent.
90276
Is $\sqrt{2}\in{\Bbb Z}[\sqrt{2}+\sqrt{3}]$ true?
27984
Square matrices satisfying certain relations must have dimension divisible by $3$
94378
Is Linear transformations $T_1,T_2 : \mathbb{R}^n\rightarrow \mathbb{R}^n$ Invertible?
1799
How many k-dimensional subspaces there are in n-dimensional vector space over $\mathbb F_p$?
10911
$A \in M_{n}(\mathbb{R})$ has inverse if and only if it's rank is n.
94929
Proof that the all bases of a subspace V consist of the same number of vectors?
62077
Prove that if $W_1\subseteq V$ finite-dimensional, then there is $W_2\subseteq V$ such that $V=W_1\oplus W_2$
64353
Does the set of matrix commutators form a subspace?
73155
Prove that for any square matrix, an invertible matrix B exists, so that BA is triangular
18145
Diagonalizable matrices with complex values are dense in set of $n\times n$ complex matrices.
25488
Let $A,B$ be $m\times m$ matrices such that $AB$ is invertible. Show $A,B$ invertible.
131998
let ${v_1}, {v_2} $ be orthonormal basis for subspace $W$. Prove that if $z$ is a vector in $W$, then
69542
Why do the $n \times n$ non-singular matrices form an "open" set?
155272
Is a matrix with $1$s in the diagonal and off-diagonal entries with absolute value less than $1$ invertible?
128760
If $A$ and $B$ two $n\times n$ matrix such that $AB=BA$, then $\dim(A\cap B)$?