Given a linear transformation T: V→W where V and W are subset of R2 which is defined as: T C₁ C₂ 2C1 +4C₂ 301 +50₂ Question : How to determine Kernel of linier transformation T?

Let T : U → V be a linear transformation. Use the rank-nullity theorem to complete the information in the table below. U R R" dim(U) 5 Ex: 5 Ex: n+2 rank(T) nullity(T) 4 Ex: 5 Ex: n+2 Ex: 5 6 5

Consider the linear transformation T: R? → R³ such that T(X) = Ax where A = 1 3 10. Is b -2 -3] 3 16 in the range of the linear transformation T? If not, why not? If so, find a -18 vector x such that T(x) = b.

Topic is Linear Transformation: Instruction: Provide the image for v and the pre-image for u of the given linear transformation: a. T: R2 -> R2, T(v1 ,v2) = (v1 , v1 + 2v2) , where v = (2,3), u = (4,12) b. T: R3 -> R3,  T(v1 , v2 , v3 ) = (0 , v1 + v2 , v2 + v3) , v = (-3,2,5) , u = (0,2,5)

Need help with this question. Thank you :)

check the image for question.

Is T linear ?  Is T one-to-one?  Is T onto?