Prove that there exists a linear transformation $T: \mathbb R^2 \rightarrow \mathbb R^3$ such that $T(1,1)=(1,0,2)$ and $T(2,3)=(1,-1,4)$
93121
How to prove there exists a linear transformation?
59055
Diagonalizable transformation restricted to an invariant subspace is diagonalizable
79537
Finding an unknown linear transformation given that $T(1,1)=(1,0,2)$ and $T(2,3) = (1,-1,4)$
127882
Proofs involving orthonormal basis
141166
How to show that when the linear transformation $\Phi =\psi \circ \phi : E \rightarrow G$ is injective, then $\phi$ is also injective?
150442
What does a linear transformation do to a vector in $\mathbb{R}^2$
118996
Prove that $T$ is an orthogonal projection
80279
Show that $S + T$ and $aT$ are linear
98824
linear transformation $T$ such that $TS = ST$
149907
$T\circ T=0:V\rightarrow V \implies R(T) \subset N(T)$
60655
$\ker T\subset \ker S\Rightarrow S=rT$ when $S$ and $T$ are linear functionals
19139
$T:\ell_2\to \ell_2, T(x_1,x_2,\dotsc)=(x_1,x_2/2,x_3/3,\dotsc)$
90435
Prove that there exist linear functionals $L_1, L_2$ on $X$
3846
Let $v_{1}=(1,-2,3),v_{2}=(0,-1,2)$. Enlarge $\{v_{1},v_{2}\}$ to a basis for $\mathbb{R}^3$.
35345
How do i prove invertibility of this linear transformation
76586
How to prove that linear transformations transforms lines into lines
71492
Matrix of Linear Transformation by right multiplication