a) Let V(R) be the inner product space and a, B E V Il a +B 12+| a - B 1?= 2(1| a |l² +I B I²) prove that. %3D b) Let V(F) = C*(C) be an inner product space with a standard inner product. {a, = (1, i,0), az = (0,1, i), az = (0,0, i)} Obtain an orthonormal basis from the set using the Gram-Schmidt steepening method.

Q: Let (u, v) be the inner product on R² generated by A = [ 6 -1 and let u = (3, −5), v = (7,4). Find…

A: We have to find <u, v>

Q: 4. Check that the following are vector spaces: (a) RN. 55 / 600 (b) CN. (c) C(N), where 2 is a…

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Q: Show that the function defines an inner product on R3, where u = (u1, u2, u3) and v = (v1, v2, v3).…

A: An inner product on real spaces V is a function that associates a number u, v with each pairs of…

Q: 3) Let V = {("), a,b ER'} (note R* = {r € R|r > 0} ). Define "addition" on V by C) + C) - G)…

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A:

Q: Let Consider the complex inner product space C³ with the usual inner product (u, v) = ₁V₁ + U₂ V₂ +…

A: Inner products space

Q: 6 Let (u, v) be the inner product on R² generated by A = - [ -1 and let u = (3, −5), v = (7,4). Find…

A: We have to find the .

Q: True or False: (p, q) = pq defines an inner product on P(R).

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: Determine whether each product is an inner product space in R3. If not, explain why. 1) = u1v1 +…

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Q: ) Let B = {1,1+x, 2+x+x2) and D Pn is the set of polynomials of degree n). a) (1+x, 1-x) be bases of…

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Q: (1) (a) Suppose V is a real inner product space and u, v e V. Prove that if ||u + o||2 = ||u||? +…

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Q: Let (u,v) be the inner product on R² generated by A = = [ and let u = (3, −5), v = (7,4). Find (u,…

A: We have to find

Q: 5. Let S be the set of all points (x11, X12, X13, X22, x23; X33) E K® such that the matrix x11 *12…

A: The objective is to determine if the set S is convex or not, where  S is set of all points…

Q: 3. Let V be a finite dimensional inner product space. If S = {u, v} is an orthonor- mal set, compute…

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Q: If on V = R² define the usual scalar multiplication « (x, y) = (« x,x y) , and addition (x1, Y1) +…

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