2. Consider the subspace im(A) of Rº, where 1 1 A = | 1 1 3 Find a basis of ker(A"), and draw a sketch illustrating the formula (im A)- = ker(A?) in this case. T

{[i :]:[ 1 0 0 0 ; :]:[: :)-[: :]} 1 1 1 0 1 1 - Let B a basis for M2(R). = 0 0 1 1 Find the coordinate vector [A]B_ relative to the basis B, where a b (a) A (а) А — с d -1 3 (b) А — 2 5

(1) Consider the basis 8-{(:) (:)} B = of R2. What is the coordinate vector of (;) with respect to B.

4 Let W = span(vV1, V2) where vi = and v2 2 . Then: (a) Find the orthogonal decomposition of the vector x = 3 (b) Find an orthogonal basis for W- (remember to justify your answer).