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1. Let B1 = {1, æ, } and B2 = {x - 1,22 - 1 -...


1. Let B1 = {1, æ, } and B2 = {x - 1,22 - 1 - 1,1} be two (ordered) bases of P2(R). Let C1 = {ēm, ēm, ēj} and C2 = {@i - ēm,
1. Let B1 = {1, æ, } and B2 = {x - 1,22 - 1 - 1,1} be two (ordered) bases of P2(R). Let C1 = {ēm, ēm, ēj} and C2 = {@i - ēm, ēz, ?i + ?2+ēz} be two (ordered) bases of R3. Suppose the matrix of T is given by [1 1 1] [2 0 1 Find the matrix of T with respect to the bases B, and C.
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м. (т) - Ti 11 Tolo 120 l B = {1, x, x²] c = {e, e, es} T(1) = 14 toe +28z T(x) = le+lez toe Lol lol T(x²) = re, toe +lezB₂ = {x-1, 2-x-1,1] C₂ = {e-es, es, e + e + ez] T(4-1) = TCX-TCD) Til T Lol L 07 -,66-8) +65 +6 (8+2+8) L- 21 - C +C =0 -C, +TO2²-x-1) = T(0) - -TO) - ² d + d₂ = -1 adi tay = -1 det dz=-1 → dy =-1-di -d,+ (-1-di) = -1 - 2d, zo ) d, 20 so dz=-1 de=0 STEB let ri lo-bill+ Palot ba LO 12 bitkz=1 -bi+P = 0 by tp 3 =2 b,=P3 b 3 tpz=1 - 13 = 1/2 Sop, =/ P2 + 1/2 =2 ů -Ind 1 - 3 3

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1. Let B1 = {1, æ, } and B2 = {x - 1,22 - 1 -...
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