Question

Please solve the following linear algebra problem. Please show all work for all parts thank you.

6. (12 pts) Show that the function T: R3 R2 defined by T | ( 7x + 4y - z T-x+3y + 2z) is a linear transformation from R3 into R2.

Answer 1

het aber and d, ß ER", then he have T (axtbp) = T[ac 22 ) + ( 1 ) ) = TI aufble) ay i+b42 azitba = Max + b) +4 (ay, +by) - (92, t62) (- Can't b22) +3 (ay, tbe) +2 (as, +b?) = at(3) + b ( 14 ) AT(22+6 TORI = a/rnithy, -3, 1tb/7212 +4 Ž) -nity, 723) 1-1₂ +3% +2%) = /rax, thay, -a3 7 b2thby - bą 1 1-anitiay, +293) + (-by t3 by +262) = 7an,t hay, -93, +76% +4 by- bę 1 l-an, tay, +2 a3, -bų t3 by +26} =/7lam, tb) + 4 (ay, +34) - (93, +'?) - cantha) + 3 cay, tby) +2 (93, +62) Maxth pla a TIKI +b Tep) & a, b GR tx, PGIR² : :. T is linear transformation