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

Q: Let B = {(1,2,3), (3, 2, 1), (0, 0, 1)}. Show that B is linearly independent and spans R3. Show all…

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Q: {(1, 2, 3),(3, 2, 1),(0, 0, 1)}. Show that B is linearly independent and spans R3.

A: Linear span: Let V represent a vector space, and S=(v1,v2,...,vn) represent a subset of V. If every…

Q: Find the cross product i x v where i = 2i +2j -3k and i = (- 8, – 6, 3). i x ở =

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Q: The scalar product 0v is 0.

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Q: Calculate the dot product, of u and v, where u = 58 î - 75 ĵ + 12 k and 34 Î – 73 ĵ - 97 k. = u.v=

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Q: Find the cross product a * b. a=(4, 5, 0), b = (1, 0, 7) Verify that it is orthogonal to both a and…

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Q: }] respectively. Let y = and u = . Write y as the sum of two orthogonal vectors, y, in the span of…

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Q: Find the cross product a x b. a = (4, 5, 0), b = (1, 0, 3) Verify that it is orthogonal to both a…

A: Given vectors are  a={4,5,0} and b={1,0,3} We have to find a×b

Q: . If u and v are nonzero vectors in Rº, why do the equa- tions u · (u x v) = 0 and v · (u x v) = 0…

A: The dot product of orthogonal vectors is equal to zero.

Q: Find the cross product a x b. a = j + 6k, b = 3i - j + 5k Verify that it is orthogonal to both a and…

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Q: Consider the two vectors u = 5i+j-4k and v=3i+j - 4k Find the cross product u x v. U XV= j+ k

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Q: Q7) True or False, and Justify your answer. If v1, v2, ... V4 are in Rª and v3 = 2v1 + v2, then…

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Q: How does the cross product i x ì relate to the vectors ở and i geometrically? Use this to compute d…

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Q: 4. Show that the vectors v1, v2, and v3 are linearly dependent, where Vị = V2 = and v3 =

A: If we have a set of vectors v1, v2, v3, ..., vn, then they are said to be linearly dependent if…