Let x 0 and y 0. (a) If xly, show that {x, y} is a linearly independ- ent set. (b) Extend the result to mutually orthogonal nonzero vectors X1, Xm- ...

Q: show that the vectors: 2,3), II

A: To prove that the vectors:     v1=(1, 2, 3), v2=(-2, 1, 1), and v3=8, 6, 10 in ℝ3  are linear…

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Q: Prove that the vectors (1,1,0), (3,1,3) and (5,3,3) are linearly dependent.

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Q: Determine a vector that is orthogonal to both (1, 4, −1) and (5, 1, 0).

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Q: Find two linearly independent vectors perpendicular to the vector 1 3

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Q: 2) Write the vector v as a sum of proj span{.…...} (v) and proj spo span{m} orthogonal set V₁,..., V…

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Q: (×q) × (gxv) + (gxg) x (xv) + (x) x (qxv)

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Q: 2. fu = and v = v1, v2, V3 > are two vectors in 3-space show k that u x v= u1 U2 U3 V1 V2 V3

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Q: Explain “ some combination gives the zero vector, other than the trivial combination with every…

A: The statement is “ some combination gives the zero vector, other than the trivial combination with…

Q: If vectors b, c and d are not coplanc then prove that vector

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Q: Two linearly independent vectors in R3 span R2, is that true

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Q: Find all vectors u such that ux(1,1,1)=(8,-5,-3).

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Q: Let y = *₁ = 0 and ū= 6 . Write y as the sum of two orthogonal vectors, ₁ in Span{u} and 2…

A: Given that the vectors  y→=0-1-2   and  u→=56-1   .

Q: Express the Vector x as a linear combination of the U's U₁ Gl , 02 [1] ·16

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

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Q: Show that if u and v are vectors in the three-space, then ||u x v||? = ||u|| ||||² – (u · v)²

A: u and v are vectors.

Q: Find non-zero vectors I and 7 that are both orthogonal to and orthogonal to each other.

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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

Q: Prove that the vectors (1,1,0),(3,1,3) and (5,3,3)  are linearly dependent

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Q: If possible express the vector v as a linear combination of V1, V2, and V3. (b) v = (0, 0, -1), V₁ =…

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Q: 7) Find all vectors v in F such that 2v + ) -)

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Q: 9. Determine whether the vectors v₁ = (1,1,2), v₂ = (1,0,1) and v3 = (2,1,3) span the vector space…

A: We know that the dimension of vector space  is 3.If the given three vectors are linearly…

Q: Find nonzero vectors a, b, and c in space such that a × b= a X c but b# c.

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Q: When is a vector incomprehensible and when is a vector irrational?

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Q: Let a and b be vectors in R" such that |la||=|b||= 2 and (a,b>=. Then ab..

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Q: If possible express the vector v as a linear combination of V1, V2, and V3.

A: If possible let pv1 + qv2 + rv3 = vp(3, -1, 2) + q(-2, 1, -1) + r(3, -2, 1) = (0, 0, 0)

Q: Show whether the vector w is a linear combination of vectors v1, v2 and v3 where --I --E --4 -- w =…

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Q: Q5) Describe the Null A by listing the vectors that span the Null space. 135 0 A= 014 -2

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Q: (b) Let a = (a1, a2,..., an) and b = (b1, b2, ..., bn) be any two vectors in R". The inner product…

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