64 = (-12), v = (24) € M₂2 0 M22. Let u = 5.1 Write w = -3 2 -5 2 as a linear combination of u and v. Show all working. 5.2 Is the set {u, v} linearly independent? Explain clearly. 5.3 Is {u, v} a basis for M22? Explain clearly.

Q: Explain why the vectors U₁=(3, 8, -8) U₂ = (-12, -32, 32) form a linearly dependent set of vectors…

A: Linearly dependent vectors

Q: Show whether or not the set of vectors B = {U, V, W} where U = V = and W = 0 is a basis for R³.

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Q: Explain why S is not a basis for R2. S = {(4, 3), (16, 12)} O s is linearly dependent. S does not…

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Q: The set B = • {1+t², −t+t², 1 + 2t+t²} is a basis for P₂. Find the coordinate vector of p(t) =…

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Q: 2,0 10 10 Find the coordinates of æ in the ordered basis B = (a, b). Hint: The preview shows the…

A: From the graph can write, x=-6,4a=-2,6b=-4,-4

Q: Let B = vector of 7 = E [V]B 0 1 00 {[%] [83] [28] [89]} 9 9 relative to B. -5 -2 || be an ordered…

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Q: 1 2 . Let uj = |0 u2 = 4 and u3 = 1 1 1 -2 (a) Show that {u1,u2, U3} is an orthogonal set.

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

Q: Explain why S is not a basis for R². S = {(-6,4)} OS is linearly dependent. OS does not span R². O S…

A: Given: S=-6, 4. We have to explain why S is not a basis for R2.

Q: Explain why S is not a basis for R2. S = {(-4, 9), (0, 0)} O sislinearly dependent. O sdoes not span…

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Q: Determine whether {v1, v2, V3} is a basis for a3. R V1 4, v 2 = V 3 = -4 8 -8 -24 Yes No

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Q: -5 -1 -7 -2 Select true or false for each statement. Let A = 2 b = [4] and c = 21 1. The vector c is…

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Q: Explain why S is not a basis for P2. S = {1, 7x, -6 + x², 2x} O sis linearly dependent. O s does not…

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Q: Let S = {V1, V2} be a basis of R? where v1 and v2 = -3 What element of R? is determined by the…

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Q: --- V₁ = 6 y V₂ Then B is a basis of: 12, B={₁,₂). H = Gen (v1, v2} Because v1 and v2 are linearly…

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Q: Show how v is orthogonal to any linear combination formed by w1 and w2

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Q: Explain why S is not a basis for P2. S = {1 – x, 1 – x², –1 – 4x + 5x²} O S is linearly dependent. O…

A: Consider the given functions. S=1-x,1-x2,-1-4x+5x2 Let S is linearly independent and there exist…

Q: Explain why S is not a basis for R2. S = {(-6, 6)} O sis linearly dependent. S does not span R². S…

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Q: Explain why S is not a basis for P2. S = {1, 6x, –7 + x², 8x} S is linearly dependent. O s does not…

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Q: In R3, let S be the set of vectors 3 S = {V1, V2, V3, V4} = -3 -2 -4 -4 a. Explain why S spans R³…

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