Matrix Multiplication: Is A Solution Possible?

[Yankel]

Hello

I have a question, I need to tell if there exist A such as:

$$A\cdot \begin{pmatrix} 0\\ 1\\ 4 \end{pmatrix} =\begin{pmatrix} 1\\ 2\\ 3\\ 4 \end{pmatrix}$$

how do you approach this kind of questions ?

thanks !

 

[Ackbach]

You already know what size $A$ must be. What would that be?

 

[caffeinemachine]

Hello

I have a question, I need to tell if there exist A such as:

$$A\cdot \begin{pmatrix} 0\\ 1\\ 4 \end{pmatrix} =\begin{pmatrix} 1\\ 2\\ 3\\ 4 \end{pmatrix}$$

how do you approach this kind of questions ?

thanks !

Define a linear transformation $T:\mathbb{R}^3\rightarrow \mathbb{R}^4$ as $T(1,0,0)=(0,0,0,0), T(0,1,0)=(1,2,3,4), T(0,0,1)=(0,0,0,0)$. Find the matrix of $T$ with respect to the standard bases. That is one possible matrix for $A$.