If w1, w2, w3 are independent vectors, show that the differences v1 = w2 -W3 and v2 = w1 - w3 and v3 = w1 -w2 are dependent. Find a combination of the v's that gives zero. Which matrix A in [ v1 v2 v3] = [ w1 w2 w3] A is singular?

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Q: ) Let B = {vi =,₂ =, V3 =}. Determine whether B is linearly independent or linearly dependent.

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Q: Determine whether the vectors v1, v2, v3 are linearly dependent or linearly independent.

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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

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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: 1. Write the vector 1 16 as a linear combination of the vectors 1 2 and 2 1

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Q: Suppose V1, V2, V3, V4, V5 are distinct, nonzero vectors in R³ = and suppose that span(V1, V2, V3,…

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Q: 2. a. In each part express the vector as a linear combination of 2+x+4x², p₂ = 1 − x + 3x², and p3 =…

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Q: 3. Determine if the vectors work. -2 are linearly independent. Show all 0 1

A: Step 1:The given vectors are: ⎣⎢⎡​1−23​⎦⎥⎤​,⎣⎢⎡​111​⎦⎥⎤​ and ⎣⎢⎡​0−11​⎦⎥⎤​ To determine whether the…

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Q: Let V1 MECANIS 3 1 11 V2 = 1 0 V3 = SCAMENTO 0

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Q: 4. Show that the vectors v1, v2, and v3 are linearly dependent, where Vị = V2 = and v3 =

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