Question

A Linear transformation T:R^5→R^4 is given as  

C1 x2 1 as C2 + 4- x5 C4 C5

How do I find the standard matrix of T, the zero space and column-space of T?

How do I find the rank and the dimension of the zero-space of T?

Answer 1

Giveu inear tanformaton 0,0101110) (0 1010,0) 0 0

0 0 0 0 0 Non-educe AT Info. pchelor-forn) 1-110 0 0 21 L

,An Rank (A) Nouw kes A is the soludton o homogeuoud iys lem (ZO-space -, meos kerA)-- ne re duce fhe mabA to elochon form 0 L 01- 0.2 0-2.ㅡㅡ0 .200 1 2 0 0

Aince m3 14 aau-free-vanable then to gutthe Aolulton then us get the Aolutan 20 dim(Ker(A)) 2