True or false? The linear system of equations $Ax=b$ is uniquely solvable for every $b \in \mathbb{R}^{n}$ if and only if det(A) $\neq$ 0
49409
Are all of the following statements equivalent? (vectors and matrices)
71203
Proving that two systems of linear equations are equivalent if they have the same solutions
106033
Solve the system in $\mathbb{R}$
61359
Set of Linear equation has no solution or unique solution or infinite solution?
122622
Does there exist a matrix $P$ such that $P^n=M$ for a special matrix $M$?
27248
If $A$ is an $m \times n$ matrix, prove that $Ax=0$ has infinite solutions $\iff$ $\text{rank}(A)<n$
10926
System of Linear Equations - how many solutions?
71833
Are idempotent matrices always diagonalizable?
149737
For which values does the Matrix system have a unique solution, infinitely many solutions and no solution?
108885
Systems of equations with a single number
130298
Why is the group of unit upper triangular matrices solvable?
63260
Matrices whose Linear Combinations are All Singular
27767
Are two matrices similar iff they have the same Jordan Canonical form?
131480
Proof that composition of invertible linear transformations is invertible (without determinants)
109117
what value of K does the system have a unique solution
33891
If $\mathbf A$ and $\mathbf B$ are Hermitian, when does $\det(\mathbf A-\lambda\mathbf B)=0$ have only real roots?
56818
Prove that if $A$ is positive, then $\exists\;\alpha>0$ such that $\langle Ax, x \rangle\geq \alpha|x|^2$ for $x\in\Bbb{R}^n$