If vectors a, b and c are coplanar, show that ↑ ↑- ↑ 11 C -->> a. a a.b a c= 0. ↑ ↑-

Q: ex/IF Ā=i-j+3k and B =2 i+6j+3K Find the vector pricâ+B) and Prj (À-B).

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Q: Let 2 = (-8,1) and To (-7, -2) Compute the following vector B Prijz To projections.

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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 cross product of two vectors u=(2, -3, 1) and v=(0, − 1, 2) is 5. O True O False

A: Here is the solution:

Q: Determine if the vectors are Linearly Independent or Linearly Dependent. -2 [1 -5 =|2.X2) = -3 ,x6)…

A: A set of n vectors of length n is linearly independent if the matrix with these vectors as columns…

Q: Find the vector in R³ from point A = (–4, 7, 6) to B = (–8, –5, 7). AB: =

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Q: (x.yız) (x,9e)x4か t. 22 P( 3-1,0) けこくりん)2

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Q: Let a = (2,3,6) and b = (3,4,2) be vectors.  Compute the cross product aXb

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Q: Write N(A) as the span of a vector (r vectors). What is dimN(A)? Why?

A: Null space, N(A) is the set of all vectors x in R^4 here, which are solutions of the equation Ax=0,…

Q: Show that the column vectors (1,1,2,4), (2,-1,-5,2), (1,-1,-4,0) and (2,1,1,6) vectors in R are…

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Q: Show that the vectors 2 -2 2 uj = 2 uz = 3 uz = 7 1 -5 -3 are linearly dependent. Find all r1, x2,…

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Q: Suppose that u and v are vectors in 3-space such that u ||= 5 and u · v= 7. Find: (a) u · u = (b) v…

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Q: Every vector of R²is linear combination of (-1, 1), (2, –2)? Justify

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Q: Let vi = (-9,9, 6). v2 = (2, 6, 4). v3 = (4,0,0) in Rº. Find a nontrivial linear relation among…

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Q: Determine whether the vectors (1,2,3), (5,6,7), (9,10,11), and (4,8, 12) are linearly independent.

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Q: 2 A : 10 %3| 0 -1 4

A: To find out solution of homogeneous set of linear equation of A's we have to find the solution of…

Q: Find a vector orthogonal to both ⟨1,−10,0⟩ and to ⟨0,7,4⟩ of the form

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Q: ) The vectors (3,0,0,0), (0,−1,2,1), (6,2,−6,0) and (3,−2,3,3) in ?4 are linearly independent.

A: solve the following

Q: Let a = (a1, a2), b = (b₁,b2) be vectors in R². The area(a, b) is given by 1b₂-a2b₁. (a.) Show that…

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Q: Under what condition for the real numbers a,b the vectors (b,-1)(2,a) are linearly related

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Q: 5 3 -2 -3 w = -3 |; A= 4 -5 2 2 -5 4 -1 . Determine if vector w is in Nul(A)

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Q: 150. Determine the real number a such that vectors a = -3i+2j and b = 2i+aj are orthogonal.

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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: Show that the column vectors (1,1,2,4), (2,-1.-5.2), (1.-1,-4,0) and (2,1.1,6) vectors in R are…

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

A: we are given 3 vectors a, b and c and we need to determine axb.c the vectors are given as--…