Question

V04 (version 967): Consider the following two sets of Euclidean vectors: {ll! -21-y+42=0 -2 -1 = 4x - y Explain why one of these sets is a subspace of Ry, and why the other is not.

Answer 1

Question ; (onsider the following tuto Sds of Fuflidean vectores, 21: - 24-y +42 - 0 W = S 1 {(3) = 82-be -yf Explain why one of these sels is a subspaces of irs and why the Chaz is 7101 ist Let B suppuse L, BEU > Yi .21 then and S Now +3dU, 0 +0= 0 BEU ax ay LEU O OLEU Test - 2x - y +42=0 -24-4, +421 -os L+B= (xtal lytyi Now We have to check (2+2) –2624 K) – (yoyd) +(212) = (–24–8442) + (-734-41+42,) - LAB EU Horw -2 (ar) – ay +4 92 = 2(2x-y +42) that is therefore it satisfies the all londitions of the subspace that is U is a subspace of R² 2nd Question: Hare W= 5(3): -261-44-y} => -2/21 = 40-4 - 22,1 = 4x4-Y How 'xtay 977 -216121)| + 4(x+34)– (y+yi) [ AS 12+211's 121 + 1211 therefore dele Bet 7 2TB Er that is it does not satisfy the subspace Test. That means it does not form a subspace. REW BEW Here B n 24B. (2+21

Question سیر C.T(2) :- fxflain which one of the following polynomial Irans famation is limegte. and why the othere is not À transforzation is said to be Suid to be lineetz Transformation T (+3) T(2) + T(B) where d, B E Domain Det (C) Here T((x)) = 3x hey + 5hcm), 7(863) – 3x91x) +5g62) 7(hra] + gc)= 3x [he] + gromo] + 5 [héa) g(], [3x hcm) + 5 h^2)+(3xg(a) +5g62)] T (h(x)) + T (9) T( choo) 3x [C(hc29]+ 5 [ech(9)] = c [34 h(x) + 512)] Therefore if forms = C T (h(9) How t linear Tran formation 2nd part T(918)) - T (Wx) = 5h (xh6o + it 5 h (2) -5 g6x)g (0) +5 942) T [ n(x) + gix)] $ [hou) i gw] [ héx) +gro9]+ 5[ar 9) + 918] - 5[ hưx) ha)+ bcu) géx) + gradhéon) t grogén)] * T (16)) + + (gox) +5[ht 2) +31-2)] Thereforee T (he) - - 5 hek) hica) + 5 h6-2) does not form Linear Transformation