6 -3 1 Let (u, v) be the inner product on R generated by A = -1 and let u = (4, 3), v= (-5,3). Find (u, v). (и, о)

Q: Determine if the function defines an inner product on R², where u = (u, v) = ₁V₁ satisfies (u, v) =…

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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: If x, y and z are vectors in an inner product space such that (x, y) = (x, z), then y = 2.

A: We are authorized to answer one question at a time, since you have not mentioned which question you…

Q: 3-2. Prove the triple scalar product identity А (Вх С) 3 (АХ В): С.

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Q: (a) Use determinants to compute the area of the parallel- ogram spanned by the vectors (2, 3) and…

A: Note the results : Suppose we have two vectors u=<u1,u2> and v=<v1,v2> .Then area of…

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: 42. Rather than use the standard definitions of addition and scalar multiplication in R®, let these…

A: The given question can be solved as shown in step2.

Q: D = 3 u=(9,-4); || u || = -√97 u=(9,-4): || u ||= √97 u=(9,4): ||u||= -√97 u= (9,4); ||u||= √97

A: given u has initial point P at (0,0) and terminal point Q at (9,-4)

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: Find (u, v), ||u|l, ||v||, and d(u, v) for the given inner product defined on R". u = (3, 0, 1), v =…

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

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Q: Use the inner product (u, v) = u,V1 2u2V2 to find (u, v). + u = (6i, -i) and v = (i, 7i) (u, v) =

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Q: Find the modulus = (ii) -1+3i 2-7 O Locate the numbers Z,+7 and Z,=Zz Vectorially when : + bi) ž,-…

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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: Find projvu and projuv. Use the Euclidean inner product. u = (-1, 2, 1), v = (1, 2, 1) (a) projvu…

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Q: Determine whether (u, v) = (u, u₁v₁, v2) is an Inner Product on R².

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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: Compute the dot product (7, 6, 8) - (4, 10, 8).

A: To find - Compute the dot product 7, 6, 8·4, 10, 8

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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Q: Find projyu and projuv. Use the Euclidean inner product. u = (-1, 2, 1), v = (1, 2, –1) (a) projyu…

A: Given u = (-1, 2, 1) and v = (1, 2, -1)

Q: Let B={ }].[],:)} 3 2 LU} be basis for IR? 2 Find [V]a where 15 6.

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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