Let A = Show that A can be diagonalised. Then, compute A°.

Q: Find the coordinate vector of p relative to {p,» P;» P3} for P,. the basis S =

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Q: Find u, , the component of u along v.

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Q: Let a = 2i +j- 2k and b = 2i + 4j + 3k %3D (а) Determine whether a b and a +b are orthogonal,…

A: To fins a) and  b)

Q: et P E L(C") be defined by, P(z1,..., zn) = (zn, Z1,.….., Zn-1) Determine whether or not P is…

A: Let P∈L(Cn) be defined by   P(z1 , . . . , zn) = (zn , z1, . . . , zn-1)Determine whether P is…

Q: Find the unit vector e, if i = ( – 2, 2) ey =

A: Given: v→=-2, 2 To find the unit vector ev→ The formula to calculate unit vector is ev→=v→v→

Q: photo attached

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Q: What is [v]B, the coordinates of v = with respect to the standard basis B : of R?? Ex: 5 : [v]B =

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Q: Let a = and b =. Show that there are scalars s and t so that sa + tb =. You might want to sketch the…

A: Here, given that a=-5,2,1,b=-3,-4,3. To find scalars s and t such that: s a+ t b=-7,-18,11 That is:…

Q: Any vector in R perpendicular to -3 can be written in the form t, for some s, t eR

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Q: А D. В

A: In the given image,  For first vector, direction is pointed towards point B, through A. So, this…

Q: for what value of Ca) will the Vector ū = -41-8)4ak,ū =ei+4j-5k are parallel

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Q: Let ā = 2 and b a) Find the area of the parallelogram formed by the two vectors.

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Q: Rearrange the formula to make v the subject. V - u t = a %3D V =

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Q: Prove that for every pair of vectore XERn and YER's llocl·llyll.cosd where I is the angle between x…

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Q: Let E, F E R3. Show that E = F if and only if E. A = F·A for all vectors A E R³.

A: Given that E→,F→∈ℝ3. Show that E→=F→if and only if E→·A→=F→·A→for all A→∈ℝ3.

Q: Use the polygon law of addition to draw the resultant vector ( å + b) + ở for the following yectors.

A: The given vectors are added

Q: Represent the following equations in R? by a vector-valued funetions. (a) (a-h) + (y - k) = r (r-h)…

A: We will use vector valued function of standard equation  x2+y2=a2 rt→=a cost i→+ a sint j^    i.e.…

Q: Given the vector v has an initial point at (-8, 5) and a terminal point at (-3, –1), find the exact…

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Q: Write the projection of 2î +3j-k along the vector î+j.

A: Given that: 2i+3j-k along the vector i+j.

Q: 3 (c) Let ¤ = Find the vector in col(A) which is closest to T. 2

A: Consider the matrix  A=[1-1414-21421-10]We first see whether the colums of A are linearly…

Q: Given u = and v = , sketch u - 2v and identify the direction (from standard position a.k.a. (+)…

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Q: Use a graphing utility to find u × v, and then show that it is orthogonal to both u and v.u = 4i +…

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Q: Let a = ci + j and b = 3i + 3j. Find c so that a and b are orthogonal. %3D C = i

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Q: al of the vector î + xj along t

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Q: The vector êr and êe in terms of î and ĵ is given by êr = î cos e + ĵ sin 0, %3D and êe = -î sin 0 +…

A: True

Q: Is it true that if x is orthogonal to v and w, then x is also orthogonal to v − w? Explain your…

A: Given that 'x' is orthogonal to 'v' and 'w' . This implies x,v=0and x,w=0

Q: Consider the vectc 5, as shown in the Write the vector in , where a and b ar places.

A: It is given that the magnitude of the vector is. =5 and the points are  (a,b)

Q: Let u = 3j - 2k and v = 2i + 5k. Calculate cose where between u and v. is the angle

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Q: b. F= 300 N 1m 1 m 1m

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Q: Use a graphing utility to find u × v, and then show that it is orthogonal to both u and v.u = 2i + j…

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Q: Given vectors A, B, and C, construct 3C – ½ (2A-B) graphically in the provided box.

A: The given vector can be drawn with the help of triangle law of addition in vectors,…

Q: If u and v are orthogonal, what is the magnitude of u × v?

A: We define the cross product of any two vectors as :                            |u×v|=|u||v|sinθ…

Q: Let FE R?. Show that F = õ if and only if F. Ã=0 for all vectors Ā E R?. [This is a proof, be sure…

A: Answer

Q: Find the cosine of the angle between the vectors P1(x) = 1 + 2x – x² and p2(x) = -1 – 3x + 2r² with…

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Q: Use a graphing utility to find u × v, and then show that it is orthogonal to both u and v.u = −2i +…

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Q: State the vector quantities shown on the image below. AB = ( CD = ( D.

A: Given query is to find determine the vector quantities.

Q: A vector collinear to ū= is: a. d. 1,-2,-3> b. -1,2,3 > e. [K C.

A: Solution is here

Q: With T defined by T(x) = Ax, find a vector x whose image under T is b . 1 -3 2 6. -4 -7 -5 3

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Q: photo attached

A: The given vector is,

Q: Find a and b such that v = au + bw, where where u = (1, 2) and w = (1, -1). %3D v= (0, 6) %3D b =

A: Explanation of the answer is as follows

Q: Given the following points, determine the vector equation defined by having point A as initial point…

A: RCS- Rectilinear Co-ordinate System CCS-Cylindrical Co-ordinate System SCS- Spherical Co-ordinate…

Q: Find a nonzero column vector u such that Cu = 4u.

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Q: Let A = -4i – 2j + 4k and B=6i – 3j. (a) Compute cos 0, where is the angle between A and B. (b) Find…

A: We have to find

Q: D. B

A: We have to find

Q: Let a = and b =. Show that there are scalars s and t so that sa + tb =. You might want to sketch the…

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Q: Let a = and b =. Show that there are scalars s and t so that sa + tb =. You might want to sketch the…

A: a=-2, -1, 0b=-4, 1, 3sa+tb=s-2, -1, 0+t-4, 1, 3=2, 4, 3-2s-4t=-2s+2t=1 ...(1)-s+t=4 ...(2)3t=3…

Q: Ex.2. Show that the Serret-Frenet formulae can be written in the form dt = W X t, ds dn = W X n, ds…

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Q: ii) Write i = ū|| + ū̟ where ūj is parallel to ở and ū̟ is orthogonal to 7.

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