(1) Recalled that for ₁, U2, U3, U₁ € R¹, then the span of these four vectors are defined as Suppose span {0₁, 0₂, 03, 0₁} = {av₁ + bû₂ + cũ3 + du: a, b, c, d = R}. --0---0 = = are in the set called 2 3 7 V3 Determine whether the following vectors in Rª (). = (O) 3 and ₁= () span {1, 02, 03, 04₁}. Hint: You should make an argument that minimize the amount of computation, and don't have to solve some equations 5 times. Does the given set span R¹?

Q: ▶Suppose V₁, V2, V3 is an orthogonal set of vectors in R5. Let w be a vector in Span(V₁, V2, v3)…

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Q: 2.) Wrile pach vector below of the vectors in s.Cif possible), 0s a linear combination 5=d…

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Q: Suppose V₁, V2, V3 is an orthogonal set of vectors in R5. Let w be a vector in Span(V₁, V2, V3 )…

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Q: Suppose V₁, V₂, V3 is an orthogonal set of vectors in R5. Let w be a vector in Span(V₁, V2, V3) such…

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A: Let S={u,v} be a linear independent set and generate W . Then W=span{u,v} .

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Q: Suppose v1, v2, v3 is an orthogonal set of vectors in R°. Let w be a vector in Span(v1, v2, v3) such…

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Q: What if the vector v was [ 7, 11, 3]

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Q: 5.) Let V₁ = - -2 V₂: Is b a linear combination X₁V₁ + x₂ V₂ = b. 5 b=4 of v₁ and v2; that is, does…

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A: Given,  a→=-5,2,-3,  b→=7,-4,1 , c→=x,-2,z

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Q: Suppose V₁, V2, V3 is an orthogonal set of vectors in R5. Let w be a vector in Span(V₁, V2, V3) such…

A: Given three vectors which span w.

Q: Consider a set of vectors S = {V₁, V2, V3} following statements is true? = {··]} Which one of the

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Q: Suppose V1, V2, V3 is an orthogonal set of vectors in R5. Let w be a vector in Span(v1, V2, V3) such…

A: Here, v1,v2,v3 is an orthogonal set of vectors in R5 and w is a vector in Span(v1,v2,v3) such…

Q: 1) Determine if the vector b can be written as a linear combination of the vectors a₁, az, and al 1…

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Q: Determine by inspection the linearly independent vectors !! O a. O b. O C. с. -8 12 4 -2 2 5112]…

A: To determine by inspection the linearly independent vectors.a -812-4, 2-3-1, 000b 51, 28c 4-26, 6-39…

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Q: 4 16 -- 12 -21 4. Is the vector in the span of the vectors 10 12 -8 and 8 ? Explain!

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Q: S= {(1,1,1), (1,2,-3), (5,-4,-1)} is a set in R'. Show that a) Sis orthogonal. b) Write w = (1, 5,…

A: Orthogonal set is the set in which dot product of two vectors is zero.

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Q: 5. Sketch the given vectors Vand W. On your sketch, draw in v v+w, and v-w. OV=(2, 1) and W=(1, 2)…

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Q: Suppose V1, V2, V3 is an orthogonal set of vectors in R5. Let w be a vector in Span(v1, V2, V3) such…

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Q: 7. Given a= [-1, 2,6], b= [0,-1, 3] and c= [2, 4, 5]. Determine a xb.c

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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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