Let V be the real vector space of all real 2 x 3 matrices. W be the real vector space of all real 4 x1 column vectors . If T is a linear transformation from V ONTO W. What is the dimension of the subspace $\{v\in V: T(v) =0\}$ ?
A)2
B) 3
C)4)
D)5
E)6
Please, help

Question

Let V be the real vector space of all real 2 x 3 matrices. W be the real vector space of all real 4 x1 column vectors . If T  is a linear transformation from V ONTO W. What is the dimension of the subspace $\{v\in V: T(v) =0\}$ ? 
A)2
B) 3
C)4)
D)5
E)6
Please, help

loser66 · Answer

@ganeshie8

loser66 · Answer

What I don't understand is if v in V, then v is a 2 x 3 matrix
Hence, no matter what dimension of T is, the image of v can't be 4x1 one.
I meant, let 
$$v=\left[\begin{matrix}a_{11}&a_{12}&a_{13}\a_{21}&a_{22}&a_{23}\end{matrix}\right]$$

loser66 · Answer

If T is 4x2 matrix, then T(v) is 4x3 one. How can I get T(v) in W?

ganeshie8 · Answer

check this http://openstudy.com/study#/updates/54d34231e4b0acc1e52e47d8

loser66 · Answer

thanks