B 2 and i = 6 Let y = Write j as the sum of a vetor in Span {ū} and a vector orrhogonal to ủ.

Consider the vectors u=(6,2,4) and v=(1,2,0) from Example 10. Without using Theorem 5.9, show that among all the scalar multiples cv of the vector v, the projection of u onto v is the closest to u that is, show that d(u,projvu) is a minimum.

Determine whether the set R2 with the operations (x1,y1)+(x2,y2)=(x1x2,y1y2) and c(x1,y1)=(cx1,cy1) is a vector space. If it is, verify each vector space axiom; if it is not, state all vector space axioms that fail.

Consider the vector v=(1,3,0,4). Find u such that a u has the same direction as v and one-half of its length. b u has the direction opposite that of v and twice its length.

Let m = (-3,1,5) and n = (5,-1,2).calculate the vector p = n - ((m*n)/(m*m))*m.

Prove that llu - vll >=llull -llvll for all vectors u and v in Rn.

To Let 2 = (-8,1) and 6 (-7,-0) Compute the following vector b Proja To Praj to projections.

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