Show that except in degen-erate cases, (u * v) * w lies in the plane of u and v, whereas u * (v * w) lies in the plane of v and w. What are the degenerate cases?

Q: Find one voctor in R' that spans the intersoction of U and W where U is the xy-plane-that is, U =…

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Q: Find inner product of u, v and || u || if u = (1,2,5) and v = (2, –3,5). (Ctrl) -

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Q: find the projection of v onto u.

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Q: Consider the collection of vectors --000 1 Is Slinearly independent? Carefully explain your answer.

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Q: 4. For vectors v and ū in an inner product space V, prove that u´ projzu and i are orthogonal.

A: v

Q: Let C be the positively oriented square with vertices (0,0), (2,0), (2,2), (0,2). Use Green's…

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Q: Show that, in an inner product space, there cannot be unit vectors u and v with <u, v > <…

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Q: Recall that R, denotes the Sorgenfrey line. Express the basis for the topology on R,?.

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Q: What is the scalar projection of á = (1,0, 1) onto b = (0, 3, 4)?

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Q: Show that every plane through the origin in R³ may be identified with the null space of an element…

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Q: Find the set of ordered pairs (T0, Yo) for which Picard's Theorem guarantees that the IVP y ry %3D y…

A: Given,            y'=xyx+y, y(x0)=y0

Q: Prove that llu + v|| = llu - vll if and only if u and v are orthogonal.

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Q: Let ā = (1,2),b = (x,y) and = (1,-2) find the value of x and y such that a is %3D %3D %3D orthogonal…

A: Given that a is orthogonal to b So a·b=0also we have c·b=2

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

A: We can find the projection in two form one is in scalar form and other is vector form. here i give…

Q: Let r = (2,-i, 1), and y = (-i, 3,1 + i) be vectors in C3. Compute (x, y), ||x||, |ly|l, and…

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Q: Is the set of (infinite number of) vectors { (0,0,c) }, where c is a real number, a vector space…

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Q: In words, explain why V is closed under addition and scalar multiplication. Since addition on V is…

A: According to the given information, first it is required to explain why V is closed under addition…

Q: Find vector x and y in R? that are orthonormal with respect to the inner product (u, v) = 4u1v1…

A: Let x=14,0, y= 12,0 Hence, by using the given inner product, we have x,y=414(0)…

Q: find the projection of u along v u = (2, 5), v = (1, 1)

A: u=2,5 and v=1,1

Q: Find the projection of u onto v.

A: Given,            u= < 2, 1, 3 > and  v= < 1, 0, -4 > and w = < 1, 1, 5 >

Q: Show that 4(u, v) = ||u+v||² – ||u – v||2 for all u, v in an inner product space V (V - -

A: Given: The given equation is, 4u,v = u+v2-u-v2 Here we know, real vector space is V so that u,v is…

Q: State why (u, v) is not an inner product for u = (ui, u:) and v = (v, V2) in R? %3D (u, v) = (u,v;)²…

A: We are given that u,v=u1v12+u2v22 for u=u1,u2 and v=v1,v2 in R2. We know that an inner product must…

Q: Suppose di ,de,..do ore distinct real numbecs det Prove ė lineerle fade pendent ere vectors in…

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Q: Find the projection of u along v. u =〈2, -3〉, v =〈1, 2〉

A: Given: u =〈2, -3〉, v =〈1, 2〉 To find the projection of u along v

Q: Let V be a real inner product space, and let u, v, w E V. If (u, v) = 1 and (v, w) = 3, what is (3u…

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Q: If ã = <!,2,37 and b=<5,0 -17, find the vector pojection of %3D %3D ŏ onto à.

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Q: Prove that if IS or thogonal to both WaXhen is orthe gonal to every it' vector 1> 1X

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Q: Find the projection of u onto v if u= (5,-3), v = (-1,4).

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Q: Compute the orthogonal projection of i = |0| onto W = Span 3

A: Here, u→=103v1→=012v2→=410

Q: Consider R' endowed with the dot product. Let W = span{u1, u2} where u1 = (1,0, 1) and u2 = (-1, 1,…

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Q: 18. Find the vector u in 2-space of length 2 that makes an angle 0 4.

A: A vector having length u→ and makes an angle θ is given by  u→ = u→cosθ i^ + u→sinθ j^

Q: Calculate the cross product assuming that u x w иxw3D (2, 6, 1)

A: Given vector u x w &lt;2, 6, 1&gt;

Q: Prove that Cl(Q) = R in the standard topology on R. %3D

A: The closure of S may equivalently be defined as the union of S and its boundary, and also as the…

Q: Show that there are infinitely many vectors in R with Euclidean norm 1 whose Euclidean inner product…

A: Dear students you have asked multiple questions. As per our policy your first question will be…

Q: Suppose {u, v, w} is an orthonormal set in R". Prove that u +v is not orthogonal to v + w.

A: The set {u, v, w} is an orthonormal set. Therefore, the modulus of each vector is 1. The vectors u,…

Q: Let II be a plane passing through the origin, and let n be a non-zero vector orthogonal to II. Then…

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Q: 2. Let W = Span {u1, u2, uz3, U4, U5, U6}, where 4 1 , U5 = Uj = U2 = u3 = ,u4 = U6 = 2 2. 4 What is…

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Q: 2. Show using only the Cauchy-Schwarz inequality that if u,vE R", then || u- v ISl u || +| v | (1

A: Solution

Q: Suppose that u and v are vectors in 3-space such that |u||= 5 and u · v = 7.

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Q: Show that there are infinitely many vectors in R'with Euclidean norm 1 whose Euclidean inner product…

A: Note: As per bartleby instruction when more than one question is given only one has to be answered.…

Q: Let u = (– 5, – 10, – 8), v = (– 5, 6, 5), and w = (1, – 10, – 1). Prove/disprove: The set of linear…

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Q: Sketch the graph of the convex hull of S. In R, let S =. :0sx<3

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Q: Let X = (!,2) and T3} U = (1,2-)inel,2,U+ jult. %3D n+1 show that X is not T - space

A: This is a problem of Topology.

Q: SHOW THAT THE SET OF POLYNOMIUMS HAS A VECTOR SPACE OF POLYNOMIALS OF A LESS DEGREE THAN “g”  (Pg…

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Q: Show that there are infinitely many vectors in R with Euclidean norm 1 whose Euclidean inner product…

A: To prove that there are infinitely many vectors in ℝ3 with Euclidean norm 1 and its Euclidean inner…

Q: Verify that (u.u2) is an orthogonal set, and then find the orthogonal projection of y onto Span (u,…

A: For two vectors to be orthogonal, the dot product should be zero.

Q: b.) Determine the os culating plane of R.

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Q: now that Reis Banach f|xl|= | ( 2 | ², 1² ) / 2 j=1 and vector space. 2h is complete.

A: We have given Rn andx=∑j=1n  ξiq12. We have to show that Rn is Banch space, vector space and…