Question

a. Determine the angle between ū and ő, if ū = (1,5); Ū = (3,4) e R2 b. Let U = {(a, b,c) a = b = c A a,b,c ER} and W = {0,b,c)|b,c ER} be the subspaces of R3. Show that R3 = vOW. c. Consider the system x + ay = 4; ax + 9y = b i. For which values of a, does the system have a unique solution? (4) ii. For which pair (a,b), does the system have more than one solution? (2) Q2. (7+7+7) a. Let G: R2 – R?be a linear map with G((1,2)) = (2,3), G(0,1)) = (1,4). Determine an explicit rule for G i.e. determine the formula for G((a,b)). b. Consider the linear map F: R2 + R²defined as below: F((x, y)) = (x - y, x - 2y) i. Show that F is non-singular ii. Determine the formula for F-1 c. Let W be a subspace of R3 defined as below W = Span{(2,1,-1),(1,2,0)}, determine a basis for wt.

Answer 1

Answer:

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