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

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…

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A: The basis in n-dimensional space is called the ordered system of  linearly independent vectors. Let…

Q: Explain why S is not a basis for M2.2. 0 1 0. S = 0 1 1 0 O S is linearly dependent. O s does not…

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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 R³. S = {(3, 1, 0), (4, 2, 1), (2, 0, -1)}

A: Linear dependent: - If a non-trivial combination of these vectors equals the zero vector, the…

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 P2. S = {1 - x, 1 - x², -1 – 4x + 5x2} O sis linearly dependent. O…

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Q: Explain why S is not a basis for R2. S= {(6, 5), (24, 20)} O sis linearly dependent. O s does not…

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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 = {(-4, 9), (0, 0)} O sislinearly dependent. O sdoes not span…

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

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

A: The given set S=-5,1,3, 4,1,6, 13,6,8, 0,4,6

Q: In part (a.) wouldn't you have to prove that U = Span(B) as well as B being linearly independent to…

A: Yes, we need to show both the parts. And the question you asked has already been proved in the…

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

A: We can solve this as follows:

Q: The standard basis S = {ej , e2} and two custom bases B = {b1, b2} and C = {c1, c2} for R? are shown…

A: Given figure is

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

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Q: 3. Let A {v1, v2, ..., Vn} be a basis for pV and n 2 2. Is B = {v1 + v2, , v2 + V3, ..., Vn + Vı}…

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Q: Determine whether S is a basis for R3. If it is, write u = (8, 3, 8) as a linear combination of the…

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Q: Explain why S is not a basis for M2,2" 0 1] 1 0 0 1 1 0 O sis linearly dependent. O s does not span…

A: Here given set as S=0101, 1010 Now a, b lies in the field…

Q: Let A = {v1, v2,.., Vn} be a basis for FV and n > 2. Is B = {v1 + V2, , V2 + V3, ..., Vn + v1} also…

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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: Explain why S is not a basis for P2. S = {1 - x, 1 – x4, –1 – 2x + 3x2} O S is linearly dependent. O…

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

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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: 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: Explain why S is not a basis for R2. S = {(6, 5), (18, 15)} O sis linearly dependent. O s does not…

A: Given: S = { (6, 5), (18, 15)} To find: Explain why S is not a basis for R2.

Q: Explain why S is not a basis for M,2" 0 1 1 0 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 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 {u, U2}, {u1,u2, U3} is an orthogonal basis for R? or R°, respectively. Then express x as…

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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 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: 2.) Determine whether S = is a basis for R³. If it is write u = (6,3,6) as a linear combination of…

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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 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 P2. S = {1, 5x, –7 + x², 6x} O sis linearly dependent. O s does not…

A: RECALL: S is basis for V if(i) S is linearly independent.(ii) S spans V.

Q: Let W¡ be the set: 1 Determine if W¡ is a basis for R³ and check the correct answer(s O A. W¡ is not…

A: Note: Since you have asked multiple questions, we will solve the first question for you. If you want…

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 P2. S = {1, 6x, –5 + x², 8x} O sis linearly dependent. S does not…

A: Basis: A non-empty subset B of a vector space is basis if a) B is linearly independent b) B spans V.…

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: Explain why S is not a basis for M, 2. -{{::}{:}} 0 1 1 0 10 0 1 S is linearly dependent. s does not…

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Q: Explain why S is not a basis for P₂. S = {1, 6x, -2 + x²,4x} O S is linearly dependent. OS does not…

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Q: Explain why S is not a basis for M. 2,2' 1 1 S = 0 0 O is linearly dependent. O s does not span M2,2…

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