Question

need help please

5) Let T be the linear transformation that projects vectors in Ronto the line through the vector I a) Find the where the standard unit vectors ē, ē, andē are sent by T. b) Use the answer to (a) to write the matrix for T c) Find the null space and column space of the matrix obtained in (b), d) Interpret your answer geometrically in terms of lines, planes or other subspaces on R

Answer 1

5) 3 T: R be R3 projection onto line through supor for veetors in Su X1 ty. I tz ) T + y Z 3 zth t16 3 is The repe given map 3 T) +1,1.2015.10 3 { 9 ج (2) (11 r (س) Teil a Tan Tom f stelt er I el te T() = te the the The

So matrix of relative to to is - ایرا A wh we cult eul Cul Cul Cul سابعا = Nall Space of (A) 3 x y ER : Ax=0 -o 구 3 {"[3] er: amarily -Y-Z 3 ER Y, Z ER y Z yi 0 tz : ZER null Su is Space of Sparmed by wh -Ź UC

Coloumn Space of A is is :NER { is The place The null Space plane baints on The aty +Z 3 16 a ty + ==o. The Column Space is The line 6 the origin and o joining 1)