4) Suppose x and y are vectors in R". Prove a) r+ >f -x->f =4(x• y) b) If x and y are orthogonal vectors in R", then.

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

A:

Q: Show that except in degen-erate cases, (u * v) * w lies in the plane of u and v, whereas u * (v * w)…

A: Show that except in degenerate cases, (u x v) x w lies in the plane of u and v, whereas u x (v x w)…

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

A:

Q: Let x, y, z be (non-zero) vectors and suppose that z = -3x+ 4y and w = -6x + 8y – 4z. Are the…

A: Solution for 1: Given that  x, y, z be (non-zero) vectors such that z=-3x+4y and w=-6x+8y-4z. Now,…

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

A:

Q: 6. List 3 non-zero vectors in R° that are orthogonal. (You must verify that they are orthogonal.)

A: See the detailed solution below.

Q: 2. 1 show thet vectors cre linecrly dependent or lineerly in dependont

A:

Q: 8. Let C = 2 c=(; 1) - (;) ()- and b = Find a 2-vector z such that Cz = b.

A: we have  C=112-1b=11   we have to find a 2-vector such that  Cz=b

Q: 4. If the projections of vector a on x,y and z −axes are 2,1,2 units respectively, and the angle at…

A: To calculate the angle we use dot product of two vectors given by Taking two vectors as U&V…

Q: 5- The value of the chiral vector of SWNTS if the n=8, m=6 and the first vector length equal to +1…

A: n=8 m=6

Q: Prove that u · v = 1/4 llu + vll2 -1/4llu - vll2 for all 4 4 vectors u and v in Rn.

A: Given Data The equation to prove is u∙v=1/4||u+v||²-1/4||u-v||².   Evaluate the right hand side for…

Q: 3. Give two nonparallel vectors that are both orthogonal to (0, 5, 0).

A: Given A = (0,5,0) Let other two vectors be of type B = (a,b,c) A.B = a.0+b.5+c.0 A.B = 5b For…

Q: If x and y are two n-vectors, then prove that 1 1 (a) x'y< I,l»,- +=1 (Holder incquality) P 9 (b)…

A: Answer :- A) Ans :-

Q: Find two vectors of norm 1, orthogonal to all the vectors u = (2, 1, 4, 0), v = (−1, −1, −2, 2), w…

A: Given data:- u=2,1,4,0v=-1,-1,-2,2w=3,2,5,4

Q: 5) Suppose that the set of vectors {ỉ, 7, w} is linearly independent. Prove that Span({ū, T}) #…

A: Given that u→,v→,w→ is linearly independent. Prove Spanu→,v→≠Spanu→,v→,w→.

Q: Show that if u and v are n-vectors, then u · v = uT v.

A: Consider the n vectors  u=u1u2u3.un,v=v1v2v3.vn

Q: Suppose e vectors. that a and b ave nonzero Under what ciraumstarces is comp= compas Under ahat…

A: According to the problem, we have

Q: 1. Use the right hand rule to determine which of the following vectors ( î, -î, ĵ, -ĵ, k, –k ) would…

A: According to Bartleby guidelines, we are supposed to do only one question. If you want more to be…

Q: 2. The cross product of two vectors u and v is. to u and to v. Thus if both vectors u and v lie in a…

A: Given two vectors u and v

Q: Verify the Cauchy-Schwarz Inequality for the vectors.u = (6, 8), v = (3, −2)

A:

Q: 10) Find two vectors of norm 1 that are orthogonal to the vectors u = and

A: Consider the provided question, u=12-23 and v=2134 Let w=ABCD be such a vector,Then, w·u=0…

Q: 8.) find a vector of norm 2 that is orthogonal to the three vectors, u=(2,1,0), v=(-1,- 1,0) and…

A: Just assume a vector and apply criteria of perpendicular of two vectors ..as I have done solution in…

Q: Show that there are no vectors u and v such that llull = 1, llvll = 2,and u·v= 3.

A:

Q: 2. Let y and u = Write y as a sum of two orthogonal vectors, one in Span{u} and a vector orthogonal…

A: y and u are given to us and we need to write y as a sum of two orthogonal vectors such that one is…

Q: 1 Let u1 = 3 U2 = -1 , Uz = ,X = then write x as sum of two vectors -3 3 on in span {u1} and other…

A: Given, u1=1101 u2=-13-1-2 u3 = 101-1 x=1-1-33

Q: Find basis for the set of vectors in R2on the line y=nx. where n is last digit of your arid number.…

A:

Q: 20. Find two vectors of norm 1 that are orthogonal to the vectors u = (2,1,-4,0), v = (-1,–1,2,2),…

A: To find two vectors of norm 1 that are orthogonal to the below vectors.…

Q: If x, y are two no vectors, then prove that |xty | || X lle y llq by = + // use Holder inequality.

A:

Q: 19 - By using the definition of the dot product, which vector is orthogonal (perpendicular) to å =…

A: Dot product of two vectors

Q: 1 Find two vectors of norm 1 that are orthogonal to the vectors u = and v = 3

A: Given problem is :

Q: The vector norm is always positive.(i.e. ||X||>0 for every vector X.) Select one: O True False

A:

Q: 4. Give an example of vectors in R3 that spans R3. (show works)

A:

Q: Obtain a Vector of mayni tude lo that has the same direction as the Vector pPerpendicular toiboth 2…

A: The vector here has a magnitude 10 and perpendicular to both the vectors, 2ax⏞-4ay⏞+3az⏞ and…

Q: The vector (1,0, 0) is orthogonal to (0, 1, 1). O True O False

A: Since you have asked multiple question, we will solve the first question for you. If you want any…

Q: Prove: For nonzero vectors ū,vER, if (dot product) ū-v=0, then ū & v are linearly independent. Hint:…

A:

Q: 8. Show that the cross product u x v of the vectors u = (-3, 5, -4) and v = (-3, -5, -5) is…

A:

Q: Show that u and v are orthogonal if and only if ||u + v||² = ||u||2 + ||v||². (Please avoid an…

A:

Q: Show that there are infinitely many vectors in R^3 with Euclidean inner product with (1,-2,4)is zero

A: Given vector is (1,-2,4) in R^3

Q: Is it always true that T(0) = 0 where the zero vectors live in the appropriate spaces? Justify

A:

Q: 3. Show that that the vector u = -5 is a linear combination of the vectors vị = 3 U2 = and v3 %3D

A: Given vectors are u=   2-5  3, v1=  1-3  2, v2=  2-4-1 and v3=  1-5  7   To show that u is a linear…

Q: 1. Do the vectors 日 span R (over R)? Justify your answer (using methods and results that we have…

A:

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

A:

Q: ): If U, U₁, U₂ are 3 vectors in a vector space V such that 13v₁ = v + 7v₂. Then, u belongs to…

A: It is provided that v, v1, v2 are three vectors in the vector space: V and 13v1=v+7v2. We need to…

Q: State the Cauchy-Schwarz Inequality and use it for solving the two vectors in R³ if = [1,–2,4] and y…

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Q: 2.2.12. Prove that two nonzero vectors x, y are orthogonal if and only if |x+y[? = [æ|2 + ly/².

A:

Q: If x = (x1, x2)T , y = (y1, y2)T, and z = (z1, z2)T arearbitrary vectors in R2, prove that xTy = yTx

A: x = (x1, x2)T , y = (y1, y2)T are arbitrary vectors in R2 .

Q: -2 - are the vectors U, = %3D Ug = %3D in M22 are lineor ly depon dent linearly in dependet.

A:

Q: Suppose that u = (0, b) is a non-zero vector in R?. Show that the line L = Span({ủ}) has Cartesian…

A: Consider the given information.

Q: The vector norm is always positive.(i.e. ||X||>0 for every vector X.) Select one: True False

A: We know that The length of a vector with two elements is the square root of the sum of each element…