3) Let C be a basis that contains vectors (−2 + 1x + 1x2 + (−1) x3), (1 + (−2) x + 4x2 + 2x3), (−2 + 1x + 1x2 + (−1) x3), (−4 + 4x + 2x + 4x3) and P = C-B Then : b = b2 = , by = ba = b4 9 3 3 * * 2 4 4 -2 4 -1 4 -1 -1 -2 4 -4 -2 -2 2-2

Q: One of the following vectors lies in span{ 2+x + x?, 3+x- 2x2} (A) 4+ x – 7r² (B) 4+ x – 4x? (C) 4 +…

A: Solve the following

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A: Linearly dependent vectors

Q: (a) Let A (b) Let A = = x = 1 1 arbitrary mx n matrix and x = = What are the row vectors and column…

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Q: [-5 -5 [-3] 1. For the matrix A 2 -3 determine (and explain why) if vector ú 3 is | 4 2 3 2 a. in…

A: GIVEN A=-5-5002-3423 to determine if vector u→=-332

Q: 3- The vectors x, = R3, are linearly independent. (1,0,1), x2 = (-1,0,1) and x3 = (-2,4, –3) in O…

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Q: If p = a₁ + a₁x + a₂x² and q = bo + b₁x + b₂x² are any 2 vectors in P². Defined function: f(p, q) ==…

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Q: at vectors （c1 - a1, c2 - a2）and （b1-a1,b2-a2）are linearly depend

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Q: { (1, 2, 1), (2, 1, 5) , (1, –4, 7) } (i) Prove that is linear dependent subset of R³. (ii)…

A: A set is linearly dependent if and only if one vector is linear combination of other vectors.

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

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Q: ether the set of vectors in P2 is linearly independent o {2 – x - 4x2, 3+ 6x + 2x?, 2+ 10x – 4x?} ||

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Q: Approximate proju and projw. -8 -7 -6 -5 -4 -3 -2 -1 proj u 5.491 projw 4.801 = vector u vector w -5…

A: Given thatWe have to approximate Projwu and Projuw.We know that

Q: 8.) Find a vectorx such that 5x-2v=2(u-5x) SOLUTION

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Q: The following question is from linear algebra : Factors the vector (6, -5, -1)t into three…

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Q: 3. Determine whether the vectors are linearly independent or are linearly dependent in P2. 1+3x+ 3x,…

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Q: Describe all solutions of Ax = 0 in parametric vector form, where A is row equivalent to the given…

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Q: Show that the vectors a = 3i−j+4k, b = i−3j−2k and c = 4i−3j+2k are linearly independent. Find…

A: The given vectors are  a = 3i−j+4k, b = i−3j−2k and c = 4i−3j+2k

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: In P2, find the change-of-coordinates matrix from the basis B = {1-3t+1²,2-5t + 31²,3 - 6t+7t²} to…

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Q: Given A= 14 4 5 -7 3-5 , observe that the second column plus twice the third column equals the first…

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Q: 4 [1] 2. Is the vector 5 in the column space of matrix A = 1 0 -2 −4 4 4 5 3 -13]

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Q: -3 -3 9. 2 Let A = -3 -6 12 and b = 3 -3 -2 13 -5 Denote the columns of A by a1, a2, a3, and let W =…

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Q: Nacho claims that every vector in R³ (vector in 3 dimensions) can be written as a combination of a1,…

A: Step 1:Nacho is correct because Every vector in R3(three-dimensional space) can be expressed as a…

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Q: Use the definition of Ax to write the vector equation as a matrix equation -2 + Z2 - 5 3 +Z4 2 4 Z1…

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Q: Determine whether or not the given vectors in Rn form a basis for Rn a. v1 = (2, 0, 0, 0), v2 = (0,…

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Q: 5. Show that the vectors a = 3i-j+ 4k, b =i-3j–2k and e = 4i– 3j+2k are linearly independent. Find…

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Q: 9. Find all real values of c such that the vectors and +3 are linearly independent.

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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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