23. Show that u + v < u + v for any vectors u and v.

Q: Suppose v, w, z are vectors in R". Show that if r and y are linear combinatio: v, w, and z, then r+…

A: Linear combination of the vectors

Q: 6. If u,v, and w are three vectors in R', describe their linear span.

A: 6. If u,v and w are three vectors in R7, we have to describe linear span.

Q: 2. Choose the linearly dependent vectors in R

A: two non zero vectors V1, V2 are said to be linearly independent if and only if aV1+bV2= 0 ⇒ a=0 and…

Q: Let x and y be linearly independent vectors in R2.If | |x | |= 2 and | |y | | = 3, what, if…

A:

Q: 5. Determine the number of vectors (x1,...,x„), such that each x; is either 0 or 1 and i=1

A: (x1,x2,...,xn) is a vector with xi is either 1 or 0.  Now, ∑i=1nxi ≥ k implies at least k of the…

Q: Find all the vectors x* that minimize||Ax – b||, where A and b are as given. [2 1] A = 2 4, l3 3] -3…

A: To find - Find all the vectors  x* that minimize Ax - b, where A and b are as given. A = 212433, b =…

Q: Verify the Cauchy-Schwarz Inequality for the vectors.u = (1, 1, −2), v = (1, −3, −2)

A: By Cauchy-Schwarz Inequality for the vectors, we have

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

A:

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: Prove that u is orthogonal to v - proju(v) for all vectors u and v in Rn, where u ≠ 0.

A:

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: 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…

A:

Q: 11. Use vectors to show that the distance from P:(x1, yı) to the line ax + by = c is |ax, + by, – c|…

A:

Q: The length of the cross product between the vectors k and -k is equal to the zero vector. Select…

A: Given that , the length of the cross product between vectors k and -k is equal to the zero is it…

Q: 18 as a linear combination of a and y Express the vector v y.

A:

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 a non-zero vector x perpendicular to the vectors 3 13 and u =| 4 -4 3

A: Let's find.

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

A:

Q: 6 2 Show that it is vectors are lineas dependent line or independent.

A:

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

A:

Q: Verify the Cauchy-Schwarz Inequality for the vectors.u = (1, −1, 0), v = (0, 1, −1)

A:

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: 2 3. Show that that the vector u = -5 is a linear combination of the vectors v1 3 2 ------ 2 U2 = -4…

A:

Q: fx and y are two n-vectors, then prove that 1 1 -+-=1 (Holder inequality) (b) xy, <,, (Schwarz…

A:

Q: Let u = (1, 3), v = (2, 1), w = (4,−1). Find the vector x that satisfies 2u −v + x = 7x + w.

A:

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

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Q: Ex: Show that if v, u, w are any vectors, then (H.W.) ux (v x w) + v x (w x u) +w x (u x v) = 0.

A: Dot Product Property :- a.b = b.a = a*b*cosθ

Q: 3. If x and y are two n-vectors, then prove that 1 (a) |x*y|< ]], \»l, - +=1 (Holder inequality) 1…

A: Given that x and y are two n-vectors. We have to prove the following :                          (a)…

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

A: Cauchy schwarz inequality -  For any vectors u and v in an inner product space V,  |&lt;u,v&gt;|…

Q: 2. -()-- () Which of the following vectors X belongs to the linear envelope [u, v], where u =1 and v…

A: vectors x belongs to the linear envelope [u, v] only if we have x = au+bv for some real values a and…

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: Evaluate The Work Done By The Force Vector, F= (6x^2+3y)I – 15yzj + 10x^2zk From (0,0,0) To (1,1,1)…

A:

Q: 2 3. Show that that the vector u =|-5 is a linear combination of the vectors vi = -4 and vz = 3.

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: 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: 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…

A:

Q: 6. Check whether Or not F= (Osxi+CysınztSinz)i is a Coservative vector - fieid

A:

Q: 12. Suppose that ú = (a, b) is a non-zero vector in R², where a ± 0. Show that the line L =…

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Q: 11) in triple cross of vectors (A x C) x B = C x (B x A).

A:

Q: A2. Express v = (1,-2,5) in R as a linear combination of the vectors u; (1, 1, 1), %3D uz = (1,2, 3)…

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Q: Show that for any two vectors u and v: = |

A:

Q: Find a vector that is perpendicular to the graph off (x, y) = 3 + 3x−y at (x, y).

A: Given: fx,y=3+3x-y The normal vector to the given graph can be determined by the gradient of the…

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…