Let W be the set of all (x1, x2, x3, x4, X5) of R° satisfying 4 2x1 – x2 +*3 X4 = 0 2 X1 + 3"3 – x5 = 0 9x1 – 3x2 + 6x3 – 3x4 – 3x5 Find a finite set of vectors that generates W.

Q: Let V₁, V2, V3 be linearly independent vectors in R". Show that {v₁ + V₂, V₂ + V3, V3 + ₁} is also…

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Q: The dot product of two vectors can be written in the form x = 00 s+ X1 X2 and y = in R" is defined…

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Q: Do question two only

A: Step 1: Assign variablesFrom the givena=⟨4,6,9⟩b=⟨−6,−3,2⟩Let:xa = 4ya = 6za = 9xb = -6yb = -3zb = 2…

Q: Find all the vectors of the family (2-jx, j4, 2-j5, jx) that are of hermitian length equal to 21.

A: Let Y=2-jx,j4,2-j5,jx Length =Y=4+x2+42+4+25+x2   Y=49+2x2 49+2x2=2149+2x2=2122x2=392x=±14

Q: Let W be the set of all vectors of the form ū = H V = [-5s- 2t] 5s + 3t 5s + t . Find vectors ū and…

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

Q: Let y = and u = Write y as the sum of two orthogonal vectors, y, in the span of u, and y, which is…

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Q: Let m = (-3,1,5) and n = (5,-1,2). calculate the vector p = n - ((m*n)/(m*m))*m.

A: here we get p=0

Q: Find the length of the vector x=x= |x|=|x|=

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Q: Find a vector orthogonal to both = 10 2 and w = 2

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Q: Find the length of the projection of 3   onto the vector -3…

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Q: Find all values of a so that u and v are orthogonal. (Enter your answers as a comma-separated list.)…

A: Since you have asked multiple question, we will solve the first question for you.  If you want any…

Q: 6. Determine if the vectors à = [−1, 5, 3], b = [−2, 4, 7], and ₹ = [10,7,1] ar are coplanar.

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Q: Use the function to find the image of v and the preimage of w. T(V1, V2, V3) = (4v2 – V1, 4v, +…

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Q: Use the function to find the image of v and the preimage of w. T(V₁, V2, V3) = (4V2 V₁, 4v₁ + 5v₂),…

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

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Q: Show that the vectors X1 = 2e2t and 2et X2 5e3t form a linearly independent set.

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Q: Suppose and are vectors such that a × b =(3, 1, 4). What is the cross product of twice of a with…

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