Define the weighted Euclidean inner product on R', (u, v) = u1v1/3+4u2v2. Calculate ((-) () 2

Q: Let A= 00 b) Say if A is diagonalisable sur Cv H E M3x3(C) such that H-¹AH is diagonal.

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Q: Let 3 = (X'X)-¹X'Y as shown in class. Let y = w'ß, where w is a column vector. Show that Var(y) =…

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Q: Show that (x, y) = 5x1y1 – 9x2y2 for vectors x = (x1, x2) and y = (y1, y2) in R2 defines an inner…

A: This question is about application of linear algebra

Q: State why (u,v) =u,³v,² +u₂³v₂² is not an inner product for u = (u,,u,) and v= (v₁,v₂) in R².

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Q: Find the projection of u = onto v = .

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Q: (H) {| R uzayı 2)

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Q: let W be an inner product space and let w1 and w2 be vectors in W. suppose ll w1 ll =5^1/2 and ll w2…

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Q: (L[u],v ) = ( Au, v)) = (Au)"C v = u"A"C v, (u,L*[v]) = (u, A* v) = u"MA* v. (9.5) Comparing these…

A: Given: Lu,v=Au,v=AuTCv=uTATCv u,L*v=u,A*v=uTMA*v   To prove: A*=M-1ATC

Q: Show that for any vector u in R^n, (u^(T))*(u) = 0 if and only if u = 0.

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Q: X = 1 X = 2 X = 3 X = 4 X = 5 X = 6 Y = 1 843 254 308 961 1,203 1,492 Y = 2 568 1,755 1,274 755 404…

A: GIven,   X= 1  X = 2 X = 3 X = 4 X = 5 X = 6 Total Y = 1 843 254 308 961 1203 1492 5061 Y = 2…

Q: Calculate the cross product assuming that u x w = (6, 3, 6) (-u+3w) x w =

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Q: s an inner product space, where (a, 5) = 4 – 5i.

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Q: ^2

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Q: Justify that (•, ·) defines an inner product on R?. the function (', ·) defined on R? as follows: U1…

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Q: Given u, v and w from question 3, find (a) the angle between u and w,

A: u = (4,0,-2) and w = (2,1,6)

Q: Find a and b such that v-au bw, nhere u-(1, 2) and w- (1. -1) v - (4, 5)

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Q: Find the component of the U along V U=(8,2), v=(3,-4)

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Q: Given vectors u=(u_1,u_2) and v=(v_1,v_2) from R^2 prove whether or not the function f(u,v) =…

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