D. Prove i [- 2,5, 1], 7 = [2,1, – 1] and w [- 6,0, – 12] are orthogonal. %3D

Q: Show that the vectors ?1 = ( 1, 1, 2, 4 ), ?2 = ( 2, -1, -5, 2 ), ?3 = ( 1, -1, -4, 0 ) and ?4 = (…

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Q: Consider the ordered bases B = {(1,2), (–2, 1)} ß = {(1, 2), (– 2, 1)} and B' = {(-7,6), (1, –8)} B'…

A: Given that  β=(1,2),(-2,1) and β'=(-7,6),(1,-8) are two bases for ℝ2.  Also give that…

Q: bäi The cross product of the vectors 3ax + 4ay – 5az and -ax + ay - 2az * ,is -3ax+11ay-7az O -3ax +…

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Q: Show every vector a in R² can be written as a linear combination of and

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Q: Suppose T E L(V, W) and v1, ..., Vm is a list of vectors in V such that Tv1,..., Tvm is a linearly…

A:

Q: 31. The vector perpendici:!at to both 3i –-6j – 4k and -3i + 2j + 2k is A A -4i + 6j + 12k B - 4i +…

A: Cross product

Q: Let x, y, and z be vectors in Cn and let a and B be complex scalars. Show that a ( z, x) +B ( z,y )…

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Q: ow that c=3i -2j1+k and d=2j+ 4k are orthogonal.

A: Since you have asked multiple question, we will solve the first question for you as per our guide…

Q: A, B, and C are 3 distinct points with non-zero position vectors a, b, and e respectively. a If a x…

A: Given three distinct points are A, B, C. with position vectors a, b, c respectively.…

Q: (a) a = (2, 6, 0) , b = (4, –1, 1) (b) a =i-j-k, b = }i+j- 4k

A: a) given that  a=<2,6,0> , b=<4,-1,1> a→=2i+6j+0kb→=4i-j+ka→×b→=ijk2604-11…

Q: 1. In R2, what is the dual cone V* if the primal cone V is V = {y1 (-3, -4) + y2 (1, -3) | y >= O}…

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Q: The vectors 3 -1 1 i = -3 11 10 + k are linearly independent if and only if k +|

A: We will find out the required value.

Q: Let a = (- 5, – 3, - 4) and b = (0, 1, k). Find k so that ā and b will be orthogonal. k =

A:

Q: Prove that (i) the three points A(1, 4, 2), B(3, 2, 4) and C(5, 0, 6) are collinear, (ii) the four…

A: (1) Given points are A(1, 4, 2), B(3, 2, 4) and C(5, 0, 6)

Q: Let S = {v1, v2} be a basis of IR? where vi = and What element of R? is determined by the linear V2…

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Q: Determine the residual and Jacc - bian needed to solve the equation d²u 2u° = 0, - dx? 1 and u(1) 0,…

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Q: find all the scalars k such that || kv || = 3, Where v = (-1, 2, 0, 3)

A:

Q: Which of the following sets of vectors in P2 are linearly dependent? (a) 2-x+4x?, 3+6x +2x², 2 + 10x…

A: (a) given set of vectors  we shall  write in matrix form  A= 2-14362210-4if rank of above matrix is…

Q: Let B be the basis of P3 consisting of the Hermite polynomials 1, 2t, - 2 + 4t“, and - 12t + 8t°;…

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Q: Find the value of k for which the vectors -4] -5 and -5 k are orthogonal. k =

A: Let the two vectors be- a →=-20-51        and  b→= -4-50k It is given that both the vectors are…

Q: Let S = {V1, V2} be a basis of R? where v1 and v2 = -3 What element of R? is determined by the…

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Q: The vectors u = (-7, 1, -2) and v = (-28, x, - 8) are parallel if and only if x = - 212 %3D Select…

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Q: If k is a real number, then the vectors (1, k), (k, k + 56) are linearly independent precisely when…

A: If k is a real number, then the vectors (1, k), (k, k +56) are linearly independent precisely when k…

Q: The vectors 3 -4 3 = 12 w = -8 5 -23 + k 7 are linearly independent if and only if k +

A: Solution:-

Q: The set B = {1 – t2, t – t², 2 – t + t²} is a basis for P2. Find the coordinate vector of p(t) = 1+…

A: The coordinate vector of p(t) relative to B will be [p(t)]B

Q: Find the orthogonal projection of y onto u. y = -3/5] - 4/5 /5 4/5 b) c) d) 2.

A: The formula to find the orthogonal projection of y onto u is: projuy=u→.y→u→2.u→ Here,…

Q: Let v (k,2k,1) and w (k,-1,-8). For which values of k are v andw orthogonal?

A: Calculation:Since it is given that v and w are orthogonal, v ∙ w = 0.

Q: In each part, determine whether the vectors are linearly independent or are linearly dependent in…

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

Q: (2) Prove that if a + b and a – b are orthogonal, then a and b have the same magnitude.

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Q: a) Determine k so that the vectors (1,–1, k – 1),(2, k, –4) and (0,2 + k, -8) in R³ are linearly…

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

Q: . Show that the vectors a = 3i-j+4k, b = i-3j-2k and e = 4i-3j+2k are linearly independent. Find…

A: Note:- We are entitled to solve only the first question, unless specified. Given vectors: a=3i-j+4k,…

Q: Find the value of k for which the vectors and 4 -4 are orthogonal. k =

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Q: Find the cross product axb. 1+9k, b- 41-j+ 3k Verify that it is orthogonal to both a and b (a xb) (a…

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Q: 8) Find the cross product a x b and verify that it is orthogonal to both a and b. a = (1, 1, -1),…

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Q: snip

A: Given Orthogonally diagonalize A=abba,If b not equal to zero

Q: 11. Let a, =3 ,b3-5 For what value(s) of h is b in the plane spanned by a, and a2?

A: We have to find the value of h

Q: 11. What is the vector which is orthogonal both to 9i + 9j and 9i + 9k? B. 81i – 81j – 81k A. 81i +…

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Q: Find all values of c so that (2, 1, c) and (c – 1, 2, 2c) orthogonal. are

A:

Q: Find

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Q: .2 The set B= {1 +t,-t-t,1+2t+t} is a basis for P,. Find the coordinate vector of p(t)= -3-5t-6t…

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Q: Let p = (2, t) and q = (3,5). Find t such that p and q are orthogonal. (Give your answer in two…

A: We will use the property of orthogonality

Q: 6. Use the scalar triple product to determine if the points A(1,3, 2), B(3, –1,6), C(5, 2,0), and…

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Q: Find the cross product ax b. a - (1, 1, -1), b= (6, 8, 10) Verify that it is orthogonal to both a…

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Q: Let B = (1, x + 2, (* – 1)", 9x) be an ordered basis for Pg. Find the coordinate vector of f(æ) = 8a…

A: Answer

Q: Find the value of k for which the vectors -5 -1 4 and -4 k are orthogonal. k =

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Q: a) Find , \pl, d (p, q), and then find the angle between them for the polynomials in P2 if p(x)…

A: a) given polynomials belong to P2 , so their basis set will be {1,x,x2}  p(x)=-3x2+2x-5 =(-5,2,-3)…

Q: Suppose that u = – 2i – 5j and v = - 3i – Compute the given linear combination of these two vectors.…

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Q: 3. Consider the following vectors: ä=7-2] +3k, b=27-3k, and a = -37 +2j. Compute the required…

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Q: Show that the vectors a = 3i−j+4k, b = i−3j−2k and c = 4i−3j+2k are linearly independent. Find…

A: Show that the vectors a = 3i−j+4k, b = i−3j−2k and c = 4i−3j+2k are linearlyindependent. Find…