Question

answer, determine whether the function linear transformation T: R² M₂,2 define as TG y z)=Rz xty Loc-32 x-y ST: P - R defined as I (at boct (x²) = a-2b +36

Answer 1

(0) T: 1R3 Mak2 define by тұ2) 9 27 HHY -37 ҡ-а. det К. С ч. 4, 71) €3 в (ч. 4, 7,) ер? Then T(*) = Зz, sety 1) ҷ-23) 4-44 т(Р) : 7, 4td, ч:32, 9-12 Now Ҝt32 ( ч, 4,7) t (2,4,77) р (чех, 24th, 21) * т«tp) 2 10 241x4, 4,1 4,7172) htъ, ttx) + (125) (4tv) -3 (Erza) (415) -C+++) + 2,1, бut) + (t12) (3%)tt+3+) (ч-+) + (9-12) ГЗ/z, t12 #4 -«) -1Т СР) - Гd=1 411) Y:37 - т :32, 12

\t Tw) te(B) 1 * Jъ2 Cray (115) (4--1)*() (ч) (:3) Therefore T Carp) & T (x) + T (B) «,»e jp3 T is not Linear frans formation. ъ Т. ?, defined by т(at bxt ex-): л-2-bt 3с. xet xa atbixx 4x2 EP₂ Р. 42+bx+ x < P, ТС) = Т (at bx+c.x-) - 2 bitc) TCP) 2 TCeztbx+c) = а2-2bzt34 <<p (at byx+x+) + (@stbx+x) > Фt) t Corv) + Cr14) - С Т (tP) 2 (ort *2) -2 tbit b2) +3 (et) (1-2 byric) + (9-22+39) 2 2 TC) TTCP). і, тер) = TC) + ТСР) и «, В€ 0, (0)

at bato ex² € P2 alt Ć EIR and x= then T(*)= a- 2b73c. Now 2 ! cº - (+ bx + x) c'at e bat ecaz T (ca) = T ( clar cbre c'ck?) c'a-2 (cb) +3 (c'c) 2 e' (a-2b13c) 2 2 e' t ca). Therefore & C'ER, XE P2 T(ca)= c'T(2) u We have from © and linear transformation. T is a