If U and V are 2 x 1 orthonormal vectors and A = UVT then the trace of A is equal to а. О b. 2 с. -1 d. 1

Q: In éàch párt, đétérmine whether the set of vectors is orthogonal and whether it is orthonormal w…

A: As this is a multiple subpart question according to the Bartleby Answering rule, only first three…

Q: For what value(s) of k are the vectors u = in R orthogonal? k v= -2

A: Here we have to find the value of k such that u=1k3 and v=k2-2-1 in ℝ3 orthogonal.

Q: find all values of the scalar k for which th e two vectors are orthogonal.

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Q: The vector E %3D —а, — 4аф + За, еxpressed in RCS and in terms of ф is E 3 (-сosф + 4sinф)ax +…

A: This question is based on unit vector conversion from Cartesian to cylindrical system.

Q: The value of the chiral vector of SWNTs if the n=8 , m=6 and the first vector length equal n/2+1 and…

A: Given that m=6,n=8to find the chiral vector of SWNT.  As we know that, the chiral vector c can be…

Q: A. Calculate the first two vectors generated by the Jacobi method. -4 1 (-6) 1 3 -1 x ={-6 x(0) =…

A: To find- Calculate the first two vectors generated by the Jacobi method. -41013-10-15x = -6-67, x0 =…

Q: Two Electric field vectors E1 and E2 are perpendicular to each other; obtain its base  vectors.

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Q: 16 Jlg wo vectors ñ and m are said to be orthogonal if ħxñ=0 ulgo O ihs o

A: Two non-zero vectors are said to be orthogonal when (if and only if) their dot product is zero.

Q: 2. Find the value of a for which the vector à = (axy – z³)î + (a – 2)x²j + (1 – a)xz²k have it's…

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Q: Let a = (-4, 5, -1) and b = (0, –3, 2). Show that there are scalars | | s and t so that sa + tb =…

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Q: +5 c) Let y = n44| and u = is Span{u} and one orthogonal to u. where n=9. "t. Write y as sum of two…

A: y=nn+4 and u=n+5n-1. We have to write y as the sum of two orthogonal vectors, one is span{u} and one…

Q: Question 7. Show that if =0 and u - = 0, then i = 0. Let i, u be two linearly independent vectors in…

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

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Q: 27. Given the vectors a and b, where a = 21 – 2j + 2k and b = 3i – j + 2k are coplanar vectors, a x…

A: Given vectors are a=2i-2j+2k and b=3i-j+2k are coplanar vectors. To find: a×b Solution: We have…

Q: 2. Consider the vectors in En : e, = (1; 0; 0); ez = (0; 1; 0); ez = (1; 0; 0); Write down the…

A: Solution :-  the given vecots are e1 = ( 1; 0; 0 )  , e2 =  ( 0; 1; 0 )  , e3 = ( 0; 0; 1 )  and  (…

Q: Let x and y be vectors in Rn, n > 1. Show that if A = xyT , then det(A) = 0.

A: Given: x and y are vectors in ℝn, where n>1. Thus x and y are given in the form

Q: \(\) The vectors u= and U= are not orthogonal if and only if x=-136 Select one: O True O False

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Q: A vector orthogonal to both u = 2i + j – 2k and v = -j+k is اخترأحد الخيارات -i – 2j + 4k .A | i –…

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Q: When decomposing the vector A= 2i - 1 + 3k into the sum of two vectors, the first is parallel to the…

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Q: Assume that 0 < a < 1 and 0 < b < 1. Find the stable vector - [';" - a 1 - ] a P = b

A: From the given information, P=1-aab1-b Let, stable vector as, w=xy

Q: 31:- A) Sind uniA vector Lr 3a tb if aijrk ち-2S-sk

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Q: Find the general solution to the following vector DE. 1 æ[t) = | -2 1

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Q: If u and v are vectors in R^n, and if v≠0 ⃗, then u can be expressed in exactly one way in the form…

A: first draw a figure as below

Q: The four matrices Sx, Sy, S and I are defined by 0 -1 where i2-1. Show that S I and SS iS,, and…

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Q: 2) If A =,find grad(div A), where r is a position vector.

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Q: Suppose that the sum of the three vectors u, v, and w shown in the figure is the zero vector. If…

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Q: 1. Show that the following vectors are linearly dependent. Uz = U3= %3D -2 3.

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Q: 1. Consider the vectors a = (1, 1, 1) and y = (1, 1, 3) in Rº. Compute æ x y. 2. Show that, for æ, y…

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Q: 5. Find the angle between the vectors (approximate to the nearest degree): u = [0, 1,1] and v = [1,…

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Q: 4 If r(t) =(1+t)3/2i+(1 - t)/2j + tk, t= 0 then the binormal vector B is

A: Consider the position vector,   rt=491+t32i+491-t32j+13tk,   t=0                      Orrt=491+t32,…

Q: If u = x2 + 2x -y and v = - 2xy- 2y, then the vorticity vector is - 3yk 10 -yk 110 YK III

A: We have to solve given problem: Concept:

Q: Compute (m +n)´ if m and n are two unit vectors and the angle between them 30°.

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Q: X/ Find The normal vector to A = 2i-3j+4K , B = i-2 j+ 5K AxB=Ñ =? ĀXB=N -3 4 = -7i-6j-K %3D - 2 Hw/…

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Q: Find the coordinate vector of p = 2 – 4x relative to the basis B = {q,,q,} for P1 where q1 = 3 + 8x,…

A: Given : We are given a vector,  p = 2-4x  and a basis  B = q1, q2,                 where,  q1= 3+8x…

Q: Let x and y are orthonormal vectors in R". Then ||x – yl| is a) o b) c) V2 d) 2

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Q: 1. Determine if the vectors e2t and e-t are linearly inde- e2t e-t pendent/dependent.

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Q: Let x and y are orthonormal vectors in R". Then ||x – y|| is a) 0 b) 1 d) 2

A: If x and y are orthonormal vector in R^n .  Then ||x-y|| is √2

Q: 3. The Gram-Schmidt process was applied to v₁ = 1 W₁, W2 and w3. Which of the following is equal to…

A: The given vectors v1=111, v2=110 and v3=100

Q: Suppose a and b are vectors such that axb=(1,

A: Given, a→ and b→ are vectors such that a→× b→=(1, 0, 2).

Q: In Fn, let ej denote the vector whose jth coordinate is 1 and whose other coordinates are 0. Prove…

A: If we can show that  {e1, e2, . . . , en} is linearly independent in Fn then we can say that  {e1,…

Q: QUESTION 2 a) Use the Wronskian to show that the set of vectors {-2x + 1, e*, cos x}

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Q: The vector E = = -a, – 4as + 3a, expressed in RCS and in terms of ø is Е 3 (-сosф + 4sinф)ax +…

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Q: Find the best approximation to z by vectors of the form cv1 + ¢2V2. 3 1 -7 -1 1 V1 V2 -3 3

A: To find  The best approximation to z by vectors of the form c1v1+c2v2.

Q: 4. Find the components of the vector with the opposite direction to that of the vector from M(2,3,5)…

A: First we need to find the vector and then find the opposite components of it.

Q: The set containing the vectors -1//3 1//3 1//3 is O1. orthonormal. II. neither orthogonal nor…

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Q: For a given vector a E R" and scalar A > 0, show that the following problem 1 minx, ||x – all +A…

A: Given: A vector a∈ℝn and a scalar λ&gt;0   To show: The problem minx12x-a22+λx2 has the optimal…

Q: If i • ( or v• (u x w) or w • (u x 7) equal to zero, then the 3, and w vectors u. are coplanar.…

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Q: Show that the vectors (1- i, i) and (2, –1 + i) in C“ are lincarly dependent over C but linear…

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Q: s such that vectors –si – 2j+5sk and 9si +j+3sk are orthogonal.

A:

Magnitude

A vector is an element with both direction and magnitude. A vector is represented using an arrow, where the arrow represents the direction of the vector and its length is represented using the magnitude. The set of vectors in space is known as vector space. The vectors can be added, subtracted, multiplied, and divided in a vector space. The image below shows a vector AB.