Suppose y is orthogonal to u and v. Show that y is orthogonal to every w in Span {u, v). [Hint: An arbitrary w in Span {u, v} has the form w = clu + c2v. Show that y is orthogonal to such a vector w.] Span{u, v}

Q: Show that the vectors i - j, j - k, k - i are parallel to a plane.

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Q: 18) a) Find a unit vector that is orthogonal to both u = and v = . b) find the area of the…

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Q: Suppose that x = (2,1,0,3),y=(3,-1,5,2), and z=(-1,0,2,1). Which of the following vectors are in…

A: A vector v is said to be in the span of the vectors v1, v2, v3, ……, vn if the vector v can be…

Q: Let w, x, y, z be vectors and suppose z = -3x - 2y and w = 6x + 2y + 2z Mark the statements below…

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Q: -3 6. Let u = 0 |and i =| 1 Find a vector ü not in span {u, v}. 1

A: A vector w→ does not lie in the span of the vectors u→,v→ if determinant of the matrix formed by…

Q: 2. If X(-2, -6, 5) and Y(3, -4, 1) are two points in R³ , determine: a) XY b) | XY | in reduced…

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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: Let w, a,y, z be vectors and suppose z = -2x - 2y and w=2x+4y+ z. Mark the statements below that…

A: Given  are vectors and  and  .To choose which of the statements are true.A. B. C. D. The span of…

Q: Let w, z, y, z be vectors and suppose z = 4x+y and w=12x+2y-3z. Mark the statements below that must…

A: The given equations are z=4x+y, w=12x+2y-3z where x,y,z,w are vectors. We have to Select the correct…

Q: Let A, B, C, D be points in 3-space with position vectors a, b, c, d respectively such that b – a =…

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Q: Let w, x, y, z be vectors and suppose z = x - 4y and w = - -2x - 4y + 2z. Mark the statements below…

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Q: Let u =[3, -1] and v = [0, 1] can you find the vector[h, k] that is not in Span{u,v}? either give an…

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