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Let T: R3 → R3 be the linear transformation that projects u onto v = (9,...

Let T: R3 → R3 be the linear transformation that projects u onto v = (9, -1, 1). (a) Find the rank and nullity of T. rank nul

Let T: R3 → R3 be the linear transformation that projects u onto v = (9, -1, 1). (a) Find the rank and nullity of T. rank nullity (b) Find a basis for the kernel of T.
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TF1RDIR T(4)= proj u where v=(9,-1,1) let us C 21:34,3) T(U)= proju= Luv) <V,V? V = C2,4,3).(9,7,12 . (9,1,1). C9,-),1) v ga-Ri → 83, Ri 1 /g / 81 R2 » 83 R2 R₂ 83 R3 -g -1 g - 1 R2 » R2tgRi R3 R₃-9 RI -yg. Yoj 0 Ereduced roue echelon form of CT] 0sel i, X= 1 se- 1 2 3 Vgre -Yg X3 = er dez + o 13 23 rez وا وا۔ - Hit Hz, az are o free ,, Basis of ker(t)= ,(ه را رو) 65,0,

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