5. If a= (a1, a,), B = (b,, b,) e V,(R) then show that (a, B) = a,b, – a,b, -'a,b, + 4a,b, defines an inner product on V, (R). %3D

Q: 2. Let a, B, y be three vectors in the inner product space V½ (R) with the standard inner product…

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Q: If (0,1) ~ (-1,1) and (-1,1) ~ R. Deduce that (0,1) ~R

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Q: Find (u, v), ||u|l, ||v||, and d(u, v) for the given inner product defined on R". u = (1, 1, 1), v =…

A: Our guidelines we are supposed to answer only three subpart. Kindly repost other subpart as the next…

Q: In Exercise 22, let u = PQ\ and v = PR\ , and find (a) the component forms of u and v, (b) u ∙ v,…

A: a) Answer(a): u=(-2,6,-2) and v=(3,6,-3)

Q: 37. Suppose T and U are linear transformations from R" to R" such that T(Ux) = x for all x in R". Is…

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Q: II. a. Find the area of the quadrilateral whose vertices are G4).-4).8) using determinant. ,29 and…

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Q: Find (u, v), ||u||, ||v||, and d(u, v) for the given inner product defined on R". u = (5, 0), v =…

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Q: i) ii) (AB) = B*A', ii)AA)* = TA', (A+B)* = A* + B', %3D %3D %3D where A is a complex number and At…

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Q: Find projvu and projuv. Use the Euclidean inner product. u = (7, -5, 1), v = (1, -1, 0) (a) projvu…

A: The given vectors and .We have to find the values of the projection,a) b) .

Q: Compute the following cross products: (а) ј x (3і — ј + 2k); (b) (1,2, 3) х (3, 2, 1); (с) (і — ј+…

A: Let a Vector A→=xi+yj+zk and B→=ai+bj+ck then Cross Product between two vectors A→ and B→ is given…

Q: 5. Let M3 - {{: ahader} M22 = {" a la,b,c, de R Show that M22 with the usual matrix addition and…

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Q: 8. Which of the following are orthonormal s 1 A = {U₁ = (₂0₁2), U₂=(2,0, B = { U₁ = (2,0, ₂2), U₂ =…

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Q: В 3 {vi %3D (2, —2, 1), 22 —D (1, —3, 2), 1з 3 (-7,5, 4)}

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Q: Determine the delimited area by the graph f(x)=-2x^2+4, the axis of x and the lines x=-1 and x=2 o…

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Q: Prove that matrices H and I-H are idempotent.Note that H=X(X'X)^-1 X

A: Proof:

Q: Zet 15 and y=[1²] 6 X = 1 2 ] and Are x and dot product? explain why or why yorthogonal with respect…

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Q: 9) What transformation do you apply to get from figure B to figure C?" (x.y) - (x-2. y-3) O)-(xy-3)…

A: Here transformation is 3 unit left and 2 unit down is using for Figure B to Figure C Sothat: (x,y)…

Q: Use the inner product (A,B) = 2a11b11 + a21b21 + a12b12 + 2a22b22 to find (A, B) for 0 A - [27][221]…

A: Given A = 1-124,   B = 01-20

Q: Use the Chain Rule to compute

A: The partial derivative is ∂∂ulnu2+uv.   The partial derivative of a function with respect to a…

Q: Explain why is not an inner product for u =(u1, u2) and v =(v1, v2) in R2 when = u1u2 + v1v2 using…

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Q: (b) For each of the symmetry operations in Dzh, identify a "complementary" operation, A, that…

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Q: 7) Under the bilinear transformation w=u+iv = the real axis of the z-plane is mapped to the…

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Q: Let (u, v) be the inner product on R² generated by A = 1=[ A and let u = (3,-4), v = (-4,5). Find…

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Q: 7. Let V={(x,y) x,y € R}. Suppose addition and scalar multiplication are defined using the following…

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Q: For which transformation would triangle RST have image R'S'T'?

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Q: vectors in R" It is known that there is a single solution to the equation x,v, +…+x,v½ = w Prove…

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