Explain why S is not a basis for R³. S = {(3, 1, 0), (4, 2, 1), (2, 0, -1)}

Q: Explain why S is not a basis for R2. S = {(-3, 6)} O sis linearly dependent. O s does not span R². O…

A: We have to find out

Q: Explain why S is not a basis for R³. S = {(8, 6, 13), (6, 1, 4), (3, 1, -5), (0, 8, 3)) OS is…

A: Definition of a basis of ℝ3 : A set S is said to be a basis of ℝ3 if  i) It is linearly independent…

Q: Explain why S is not a basis for R2.S = {(2, 3), (6, 9)}

A: We know the basis of R2 = {(1,0),(0,1)} So it has 2 elements So, another basis of R2 also must have…

Q: 2. Let L1 bg 3D (-1,2, 1,3, 3), сі %3D (3, —4, 0, — 4, 3), сэ %3D Find a basis of Lin L2 and L1+ L2.…

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Q: Q8) Explain why S is not a basis a) S = {(2,1,–2), (–2, –1,2), (4,2, –4)} for R³ b) S = {2,2,x +…

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Q: Which of the following is a basis for R2? (a) {(1,-1),(-1,1)}  (b) {(1,−1),(1,1),(−1,1)}  (c)…

A: Let V=ℝ2. Identify the basis of ℝ2.

Q: Explain why S is not a basis for P2. S = {1 - x, 1 – x², -1 – 3x + 4x²} O is linearly dependent. O s…

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Q: Explain why S is not a basis for P. S = {1 – x, 1 – x², -1 – 2x + 3x?} %3D O S is linearly…

A: We will check if the vectors given in set S are linearly independent or dependent also determine if…

Q: Explain why S is not a basis for R². S= {(-4, 3), (0, 0)} O is linearly dependent. s does not span…

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Q: Explain why S is not a basis for P2. S = {1, 2x, –4 + x², 3x} O sis linearly dependent. O s does not…

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Q: a' Find the value of a for which S forms a basis for R3.

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

A: Given that - S = {1-x, 1-x², -1- 6x + 7x²}

Q: Explain why S is not a basis for R². S = {(2, 1), (4, 2)} O Sis linearly dependent. S does not span…

A: Let S=2,1,4,2 Since if S is basis of R2 then S is linearly independent and S spans R2 . Let S is…

Q: Explain why S is not a basis for R2. S = {(6, 1), (24, 4)} O S is linearly dependent. O s does not…

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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: Explain why S is not a basis for R3.S = {(7, 0, 3), (8, −4, 1)}

A: Basis definition:

Q: Explain why S is not a basis for R3. S = {(1, 6, 4), (1, 3, -5), (6, 8, 13), (0, 7, 5)} O sis…

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Q: Explain why S is not a basis for R². S = {(-5, 7)} O Sis linearly dependent. O s does not span R2. O…

A: use the definition of linear independent set. and of basis.

Q: Explain why S is not a basis for M2,2- s={: :}[::} 1 0 0 1 O sis linearly dependent. O s does not…

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Q: Explain why S is not a basis for R2.S = {(4, −3), (8, −6)}

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Q: The vectors x1 = (2, -3, 1), x2 = (1, 4, -2), X3 =(-8, 12, –4), x4 = (1, 37, -17), and x3 = (-3, -5,…

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

A: We will explain the reason.

Q: Explain why S is not a basis for R2. S = {(4, 3), (12, 9)} S is linearly dependent. O s does not…

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Q: Explain why S is not a basis for R2. S = {(-5, 4)} O is linearly dependent. O s does not span R2. O…

A: The given set,  S=-5,4

Q: Explain why S is not a basis for R2.S = {(6, −5), (12, −10)}

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Q: Explain why S is not a basis for R3.S = {(1, 1, 1), (0, 1, 1), (1, 0, 1), (0, 0, 0)}

A: To Determine S is not a basis for R3.S = {(1, 1, 1), (0, 1, 1), (1, 0, 1), (0, 0, 0)}

Q: Is R={(2,0,1), (2,-1,1), (4,2,0)} a basis for R²? Yes or No? Justify or give/find a counterexample.…

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Q: Explain why S is not a basis for P,. .2 S = (1 - x, 1 - x², -1 – 8x + 9x²} O s is linearly…

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Q: Explain why S is not a basis for P2. S = {1 – x, 1 – x², –1 – 3x + 4x²} O s is linearly dependent. O…

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Q: ...... Explain why S is not a basis for M, 2. 1 0 0 1 Os is linearly dependent. O s does not span…

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Q: Let A = {v1, vz, - also a basis for pV? How about the converse, i.e. if B is a basis for FV, is A…

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Q: b) Find the value of k such that (-1,1,1), (1,1,1), (1, -1, k) form a basis of R²

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Q: Explain why S is not a basis for R3.S = {(1, 1, 2), (0, 2, 1)}

A: To determine: The set S is not a basis of R3 S = { (1, 1, 2), (0, 2, 1) }

Q: Show that S = {(i, 0, 0), (i, i, 0), (0,0, i)} is a basis for C

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Q: Explain why S is not a basis for R2. S= {(3, 5), (1, 0), (0, 1)} O sis linearly dependent. O does…

A: The given set S=3,5, 1,0, 0,1

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: Show that B = {v1=(1,0,0), v2=(3,7,-2), v3=(0,4,1)} is a basis for R3

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Q: b) Let v1 = (1,2,1), V2 = (2,9,0) and vV3 = (3,3,4). Show that S = (V1, V2, V3) is a basis for R³.…

A: Explained below...

Q: Explain why S is not a basis for P2. S = {1, 2x, -5 + x², 9x} O sis linearly dependent. O s does not…

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

A: The set S=-3,4 is not a basis for R2.

Q: Explain why S i not a basis for P2. s = {1 - x, 1 - x2, -1 – 2x + 3x?} O is linearly dependent. O s…

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Q: Explain why S is not a basis for M2,2.

A: We have given a set of the matrices;

Q: Explain why S is not a basis for R. S = {(6, 8, 13), (1, 3, -5), (1, 6, 4), (0, 8, 7)} S is linearly…

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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: Explain why S is not a basis for R2. S = {(2, 5), (8, 20)} O Sis linearly dependent. O s does not…

A: Let's find.

Q: Explain why S is not a basis for R2. S = {(2, 1), (4, 2)} S is linearly dependent. S does not span…

A: Here given ℝ2 is vector space S is a subset of ℝ2. S=2, 1, 4, 2

Q: Explain why S is not a basis for R2. S = {(-4, 2)} O sis linearly dependent. Os does not span R. S…

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Q: Q8) Explain why S is not a basis a) S = {(2,1,–2), (-2,–1,2), (4,2, –4)} for R3 b) S = {2,2,x +…

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Q: Explain why S is not a basis for R. S = {(6, 8, 13), (1, 6, 4), (1, 3, -5), (0, 5, 3)} O s is…

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