Question

Find a matrix M such that the linear transformation T:R5 → R4 defined by T(x) = Mx has the property that its kernel, ker(T)， is given by ker(T) {1: ER5 @1 - 3c2 = 0, c3 - 2c4 = 0 and c5 and its range, R(T), is given by R(T) - {(:) - ༠ ༠ ༠ ༡ e R4 | u + c + + ཀྱ =

Answer 1

First we the basira of KerT. will find * ERS Ker (T) = و در محور محمد کم They ~ 224 = 0 and ag 20% 15:05 Let ** Ekert the we have 15 2,-3d, g 214 and ^2=0, and 139) 3 0 0 basic for Ker T -61 0 extend this 0 basis for IRS 200.00 O a basis for IRS 0 rouch that 000 (1) a way that other three vectors in should belong to r(t). they T T 0 0 0 0 Let Y = "లేరు az ER as مر مر گیم چی (@,-342) 1:|:ཀྱི བ ། + ag OOOO

Therefore 0 6 ངན ནང་བའི་ནང་ནས་ ད ན པ ཕ བ ན པ : དག ། གངས་ཅན་ ( )གས། - – yon དེ کو 0 0 [Francis ame] ) d - Sa -athan ） ན 5 ༤། - 56 2taz-29 ie ༽ az ag ༽ ཅ O Gང ད -5ཡཾ། -ཡེ ན 50 ན oང-2 os+ 2 ад +45 - 5 madrix given by - ༦ تم میری مدمی OO00 O G G3 0 5 ༈ ༠ Note: The matrix will vary for different clipices of basis for extending the basis for its and for ralues o enden T.