Suppose a vector y is orthogonal to vectors u and v. Show that y is orthogonal to the vector u + v. Let W = Span{v1,..., Vp}. Show that if x is orthogonal to each v;, for 1

Q: If x is an n-vector, show that x + 0 = x.

A: Given, If x is an n-vector.

Q: The polynomial of degree 3, P(x), has a root of multiplicity 2 at x=5 and a root of multiplicity 1…

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Q: 3 Given that u = 4i+ GJ and Iv[ = 2, find vif u and V are or thugonal to each other.

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Q: Let u = (2, −1, −1) and v = (5, -3, 3). A vector with integer components perpendicular to ū and v is…

A: <-6, -11, -1>Explanation:Step 1: Determine how to find the perpendicular vector To find a…

Q: ? (2,3), (0,0) }

A: Let S=2, 3, 0, 0. We need to find whether the set S spans a line or all of ℝ2.

Q: Determine if u = (4,3) and v = (1/2 , - 2/3) are orthogonal, parallel or neither.

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Q: Let u = (2, 0), v = (-2, -4), and w = (-4, 1). Find the vector æ that satisfies 4u – v+ x = 9x + w.…

A: Solution:-

Q: Let ū = (3,2), v = (-2, –2), and w = (-4,3). Find the vector x that satisfies 5u – v +x = 7x + w. |…

A: Given that u→=3,2v→=-2,-2w⇀=-4,3

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Q: Let X and Y be points in R³. Let P be a point on the line segment joining X and Y such that the…

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Q: If a = (5, 0, -1), find a vector b such that compab = 5. b =

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Q: Determine whether the set of vectors Q={(-1,1,1).(-1,0,2).(1,2,3)} spans R'.

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Q: Let v = (7,8). Suppose w E R2 is perpendicular to v, and that ||w|| = 9. Find both possible vectors…

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Q: Suppose that u is a unit vector which is orthogonal to some other vector . Then u (u + v) + ||projzu…

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Q: Let u = (2,0), v = (5,4), and w = (2,3). Find the vector that satisfies 10u-v+x = 8x+w.

A: Given u = (2,0), v = (5,4), and w = (2,3)& 10u-v+x = 8x+w

Q: show that the vectors V₁ = (2,0,- 2, 1) > V₂ = (3,1, -5,0) and V3=(2, 2, -6, -2) form Linearly…

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Q: Let v1 = , v2 = , w = vectors ∈ R2. Does the set {v1, v2} span R2?

A: given a set of vectors v1 = <0, 1>, v2 = <-1, 0>we need to find that does the set {v1,…