Question

Please solve it in very detail, and make sure it is correct.

C Mathx R Result X Relux C Gel xC CW X CLS- X > Sulux لا اداء 3 Soluli x MHX S X Full X + .app.Acark.comstudent/assets/math-2203-770-final-exam-2020 OM Q10 (5 points) Apply Gram-Schmidt orthonormalization process to transform the basis My Courses {(0:1, 2), (2,0,0), (1,1,1)} for R3 into an orthonormal basis. Use the vectors in the order in which they are given. Linear Algebra II (MATH-2203-7... Applied Math for Business and ... + Drag and drop your files or Click to browse... Q11 (4 points) Let T :V W be an isomorphism. Prove that if {w1, 2, ...,Wn} is a linearly independent set in W, then the preimages of {u, un,...,} is a linearly independent set in V Time left Show © Help + Drag and drop your files or click to browse Type here to search 1 9 e ENG 33 PM 2020-37-30

Answer 1

Then . Q. 10. The given basis is { } } } where 5,= (0,1,2), = 12,0,0), z = (1,1,1) Let {5,2 5} be the corresponding ortho normal basis. VE 110,1 14,42(0)+cu+(2)*= 0+1+435 » IqU-S5 .: (0,1,2)=(0,5 ) W = ū- (927) Ý = (2,0,0) – ((2)(0)+(0)() + (-)() (0, ' ) =6,0,0) - olas ) = (2,0,0) 11h 112 = (2) ²7 (0)7 (0)² = 4 11 W 11 = 5472 1 W4 Ź (2,0,0) = (100) W = ] - <ūz, > - <53, 2Ą = (1, 1) – (((0+014 #s) +(1)(73)) (0 1a) -(1/2)+(1)(0)+(180)) (1,0,0) = 11,01- (ots })-1(1,0,0) -(1,1)-( 0, $ $)-(1,0,0) = 10, §, 5) W 12=1057+(13)+char as to $ => 1!= foto 3. va eh (3)= (o iš T's) :An ohonored basis is for 27}={( 03).(0,0,0), (08} isomorphism. To prove: If {m, we was is a linearly independent set in W, then the preimages of {w, ų - } is a linearly independent set inv. Proof: Given: T is an isomorphism one to one and onto. for W, Wz, - - Wh EW, there exist i R... The such that in = 7(W) = T(U), y = T(F) .... W = T(F) Qoll. Given: T: VW is an . Tis

Let a, ai tahun = anell, such that attqų+agt rank = 5 a, ut qutqů + > T(autąų taugt .. tau = T(0) → a. T(F) +9T({}+Q₂ T(F) tanT(F) = 0 T is a linear transformation; a witaw tanzt and Tol= » 9,=0, go, ag=0 au 20 {:{w, wz, W3,... Why is a linearly [5.55 ... In} is a linearly independent set. independent set} tawa