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6. (a) Let V be a vector space over the scalars F, and let B = (01.62, ..., On) CV be a basis of V. For v € V, state the defi
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6 Ca Zet B = (bi, be . by be basis of over F. Then, o a vector de ev can be expressed as = ki bet kabet - et knibh The Co-ordNow, 3+*+2017+4x3 = a (1) +3 CC) to cc td C 3+x - 2167483 a+bx+coc? + da? for two polynomials to be equal the Coefficients of(c) P(x) = 3+2 – 2x tus oli The given basis or are - 8 = (1, 1-X 1-ste, le tex3] Now, 3+x-2xt uses = aci) + b (1-x) +Ccrets 2-b-C-d = 1 eld = -2 वडप - (d=-4 c+d=- [c=2 and And -b-c-d=17 16 = 1 aul at&tetel = 3 => a=4 Co-ordinates vector of P(x) wisat

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