To express the vector =(1.2 -6) as a linear combination of three vectors ,- (0.1. 2), v= (1,0.2) and w= (1,2.0) ,the corect statement is: O t= -u-v+2w O t= -2u-2v+2w O t= -2u-v+2w O t= -2u - v+w

Q: Which of the following pairs of vectors are linearly independent? Ou = (1,0) and w = (0,2). Ou =…

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Q: In 3-D, let L be a line that does not pass through the origin. let v1, v2, and v3 be three vector…

A: We have to decide there vectors v1, v2, v3 are linearly indipendent in R3 or not.

Q: 2 Write the vector x= as a linear combination of the vectors -1 1) u=0 |, v=| 1 w= 1 1 N O H O O

A: Consider x = au+bv+cw then 20-1 = a100+b110+c11120-1 = a+b+cb+cc On comparing the coefficients , we…

Q: Suppose vị and v2 are vectors with |v1| = 2, |v2l = 3, and vị · v2 = 5. Let v3 = proj,, v2, V4 =…

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Q: The normal vector to the vectors u = (2, 1, 1) and v = (1, -1, 3) is:    4i - 5j + 3k  4i - 5j -…

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Q: Consider the following vectors: -1 -3 -2 3 -3 4 8 For each of the following vectors, determine…

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Q: Express the vector v = -12 -28 as a linear combination of x = 2 [² and y= -1 -6

A: We can write the answer in the below steps.

Q: Refer to the vectors u, to ug. -5 1 1, u2 = u3 = U4 = -5 U5 4 4 Compute projs u8, where s = span{u5,…

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Q: Let x,y,z be (non-zero) vectors and suppose that z=4x−4y and w=12x−12y−4z. Are the following…

A: A vector is a span of vectors when the first one can be written as the linear combination of the…

Q: as a linear combination of x = 7 4 and y = -3 Express the vector u -2

A: NOTE: Refresh your page if you can't see any equations. . write both vectors x and y in the matrix…

Q: Let v = -7i - 7j-3 k and w =-3i+ 4j +6 k. Then the vector v – w can be written as

A: note : vector addition or subraction can be performed as  a⇀+b→ = (ax+bx,ay+by,az+bz) similarly for…

Q: Which of the following sets of vectors in P2 are linearly dependent? (a) 2-x+4x?, 3+6x +2x², 2 + 10x…

A: (a) given set of vectors  we shall  write in matrix form  A= 2-14362210-4if rank of above matrix is…

Q: Show that the vectors 1 – t,1+ 2t² , t² +t+1, t² + 2tare linearly dependent and indicate how one of…

A: Given Vectors:V1 = 1-tV2 = 1+2t2V3 = t2+t+1V4 = t2+2tgiven vectors are linearly dependent, then…

Q: Show that if {V1, V2} is a linearly independent set of vectors and v3 does not lie in Span {V1, V2},…

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Q: - Show that the vectors X, - () 5e3t and X2 = ) 2et 7et form a linearly independent set.

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Q: -11 and ỹ = Express the vector u as a linear combination of x 28 x+ y.

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Q: Consider the vectors in R2 3 2 (3) Express as a linear combination of the vectors Select one:…

A: Here we have to find the linear combination.

Q: If the vector u = 2i-3j+v3k , then the length of u is -v2 True O False

A: # we are entitled to solve one question at a time , please resubmit the other question if you wish…

Q: Express the vector in the form v = vji + v2j + v3k. AB if A is the point (-9, -5, 5) and B is the…

A: A-9,-5,5 and B-4,-12,8

Q: Determine R21, the vector from P2(5, 2,–4) to P1 (3, –1,0). 2аx + Зау — 4а, — 2ах — Зау + 4a, | 4ах…

A: Given the points P25,2,-4 and P13,-1,0. To find vector R21 from above two points. The vector from…

Q: Use the vectors a = [-1,0,1], b = [1,-1,5], and č= [0,-1,-2] to prove that a(bxč) # (åxb)xč

A: The answer is given below:

Q: Determine n so that the vectors m = (-2, 1, k + 1) and n = (0, 2, -3) are parallel but in the…

A: It is assumed that the question asks to find the value of k for which the vectors will be parallel…

Q: express each vector in the form v = y1i + y2j + y3k. 5u - v if u = <1, 1, -1>and v = <2, 0,…

A: Given vectors

Q: Suppose that ā and b are nonzero vectors. Under what circumstances is comp;b = comp;a? Under what…

A: A vector has 2 components, magnitude and direction which is represented by cos and sin angles. A…

Q: Let v1, v2, vz be the vectors in R defined by 30 -17 7 -3 v2 15 V3 = -14 -12 -14 18

A: Solution is given below:

Q: The cross product of two vectors 3i + 4j -5k and -i+j- 2k is * 3i -11j +7k O 31 +11j +7k O 31 -11j…

A: Use Cross product of vector

Q: Determine whether the vectors a = 2i-3j+ 5k, b 3i+j-2k and c=i-7j+12k are linearly dependent or…

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

Q: Determine if the vector 2 b = 3 5 can be written as a linear combination of the vectors V₁ = 1 and…

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Q: Determine whether the vector v is a linear combination of the remaining vectors. v = 3

A: (1).  The given vectors are: v→=12 ,  u1→=-1   3    and    u2→=   2-3

Q: For each pair of vectors, calculate projvu and the vector component of u orthogonal to v. (a) u =…

A: Vector components

Q: Express the vector x as a linear combination of the u's. U₁ = 0, U₂ = 5, -1.4 U3 Ox=-3u₁ +4u2 +243…

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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…

Q: What is the value of each of the constants that are part of the linear combination between the…

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Q: Express the vector v =-1 as a linear combination of the vectors -3 0,v2 4 and v3 -4 , if possible.…

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Q: 5b- За Let W be the set of all vectors of the form Find vectors i and v in R such that W = span {i,…

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Q: Determine k so that the vectors (1,–1, k - 1), (2, k,-4) and (0, 2 +k,-8) in R linearly independent.…

A: The detailed answer and explanation is given below:-

Q: Express the vector x as a linear combination of the u's. --0-0-0- 0, U₂5, U3 = -50 Select one: O A.…

A: Two matrices can only be added, if the dimensions of both matrices are the same. When two matrices…

Q: Express the vector x as a linear combination of u,, u2, and uz. – 2 3 - 2 ,x = 0 u2 = 5 u3 = – 4 u1…

A: Given u1=-201, u2=356, u3=-26-4 and x=-99-38

Q: Q3/ Show that the vectors (2i + 3j + 6k), (3i – 6j + 2k)and (6i + 2j + 3k) Are mutually…

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Q: 4. Determine whether the vectors a = 2i – 3j+ 5k, b = 3i+j – 2k and c =i- 7j +12k linearly dependent…

A: To check whether the vectors are linearly dependent or linearly independent.

Q: Determine whether the following three vectors lie on the same line in R?: и, 3 (4,6,8), и, %3 (2,3,…

A: The given vectors lie on the same line. u2=2,3,4u1=4,6,8=2×2,2×3,2×4=2×2,3,4=2u2So, u1=2u2Thus,…

Q: Express the vector 2x2 + x + 3 in the space P2 as a linear combination of the vectors p = -x2 + 1, q…

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Q: Express the vector x as a linear combination of the vectors u1, U2, and uz: 1 6. U3 = and x= 3.…

A: We will use elimination to find the values of the constants C1 C2 and C3.

Q: Consider the vectors (2, 1,0, 2], (3, 1,0, 1], [1, 1,0, -1] in R'. Decide whether they independent.…

A: Given: Vectors in ℝ4,                              2,1,0,2, 3,1,0,1, 1,1,0,-1 To find: Whether the…

Q: Determine if the vector x̄=(-12i-j-5k) can be expressed as a linear combination of ū=(1,-1,0),…

A: The solution of the problem is given in the next steps.

Q: State whether the vectors are parallel, orthogonal, or neither. 5) v = 2i + j, w =i- 2j 6) v = 2i +…

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Q: Find two vectors a and b such that projba = <4, -2, 8>. That's all the information I was…

A: It is given that,

Q: Determine whether the set of vectors in P, is linearly independent or linearly dependent. {-x + x2,…

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Q: 5. Show that if vị and vz are linearly independent vectors in R?, then any vector w E R² can be…

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Q: Can vector w = 3 be written as a linear combination of v₁ = 4 4 vector w belong to span{v₁,v₂}? V₂…

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