(a) Show that the list {p o(x), p 1(x), p 2(x), ...,p n(x),...,} where po(x) = 1, p1(x) = 1+x, P;(x) = 1+x + ..+x³, %3D ...) ... is a basis of the vector space F[x] of all polynomials with coeficients in F. (b) What are the coordinates of the vector x" relative to the basis (po(x), p1(x),..,P;(x),..)? ....

Find a basis {p(x), g(x)} for the vector space {f(x) = P₂(1) | ƒ'(−2) = f(1)} where P₂(x) is the vector space of polynomials in with degree less than or equal to 2. |p(x) = , q(x) =

Day traders typically buy and sell stocks (or other investment instruments) during the trading day and sell all investments by the end of the day. The following table shows the closing prices on September 22, 2015, of 12 stocks selected by your broker, Prudence Swift, as well as the change that day. Tech Stocks Close Change AAPL (Apple) $113.40 -1.81 ADBE (Adobe Systems) $84.66 1.34 EBAY (eBay) $25.61 -0.31 MSFT (Microsoft) $3.90 -0.21 S (Sprint) $4.40 0.02 WIFI (Boingo Wireless) $8.51 0.56 Non-Tech Stocks ANF (Abercrombie & Fitch) $21.81 -0.02 в (Воeing) $133.99 -2.03 F (Ford Motor Co.) $13.91 -0.40 GE (General Electric) $25.10 0.01 GIS (General Mills) $57.12 0.33 JNJ (Johnson & Johnson) $93.26 0.13 On the morning of September 22, 2015, Swift advised you to purchase a collection of three tech stocks and two non-tech stocks, all chosen at random from those listed in the table. You were to sell all the stocks at the end of the trading day. (a) How many possible collections are possible?…

find a basis for the range from r2 to r3 as defined by [3x1+4x2; x1-2x2; 4x1]