hello guys I can you plaese helps me out to answer those questions from 1 to 3 w

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hello guys I can you plaese helps me out to answer those questions from 1 to 3 with showing me the work of it and also write the number of the question to be able to see them and u could type them by the coputure that will be great ! thanks !

C secure https://mathcms2.asu.edu/moodie/pluginfile.php/20859/course/section/1366/242h5.pdf 242h5.pdf Solve the following problems, showing any necessary work. 1, 11 point] Find basis for W+, the orthogonal complement of W, if W is the subspace spanned by 21 -6 2. [1 point] Let i-1-4 | Note that B = {V1,U2, V3} is an orthogonal -4 basis for the subspace spanned by B. Find an orthonormal basis for the subspace spanned by B 3. Let W be the subspace spanned by Note that this basis is not orthogonal. -12-8 14 a. [1 pointj Find the orthogonal projection ofI7 into W b. 1 point] Find an orthogonal basis for W

Explanation / Answer

1.Let X= (x,y,z,w)T be an arbitrary vector in W. Then X.(-7,21,5,8)T = 0 or, -7x +21y+5z+8w = 0 or, 7x-21y-5z-8w = 0…(1). Similarly, X.(2,-6,-1,-4)T = 0 or, 2x -6y-z-4w = 0…(2). On solving these equations, we get x = 11y+7z/3 and w = 4y +11z/12 so that X = (11y+7z/3, y, z, 4y+11z/12)T = y(11,1,0,4)T +z/12(28, 0,12,11)T. Then {(11,1,0,4)T,(28, 0,12,11)T } is a basis for W.

2. Let e1=v1/||v1||=v1/(1+4+16+4)=v1/5=(1/5,-2/5,-4/5,-2/5)T, e2=v2/||v2||=v2/(484+121+4+16)= v2/25 =(22/25,11/25,2/25,-4/5)T and e3=v3/||v3||=v3/(16+4+121+484)=v3/25=(4/25, 2/25,-11/25, 22/25)T. Then {e1,e2,e3} is an orthonormal basis for the subspace spanned by B.

3. a. Let u1 = (1,2,2,-4)T,u2= (-6,-7,-12,14)T and u3 =(-9,-3,-8,11)T. Now, v = (-1,3,-17,-1)T so that proju1(v) = [(v.u1)/(u1.u1)]u1 = [(-1+6-34+4)/(1+4+4+16)]u1 = -(25/25)u1 = -u1= (-1,-2,-2,4)T .

proju2(v) = [(v.u2)/(u2.u2)]u2 = [(6-21+204-14)/(36+49+144+196)]u2 = (175/425)u2 = (7/17)u2=                   (-42/17,-49/17,-84/17,98/17)T and proju3(v) = [(v.u3)/(u3.u3)]u3 = [(9-9+136-11)/(81+9+64+121)]u3 = (125/275)u2 = (5/11)u3= (-45/11,-15/11,-40/11, 5)T.

Then projW(v)= (-1,-2,-2,4)T+(-42/17,-49/17,-84/17,98/17)T +(-45/11,-15/11,-40/11, 5)T = (-1414/187,-1168/187,-1978/187,251/17)T.

Please post 3(b) separately again.

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