Let A = {v1, vz, - also a basis for pV? How about the converse, i.e. if B is a basis for FV, is A also a basis for pV? Un} be a basis for pV and n 2 2. Is B = {v1+v2, , V2+V3, %3D %3D ..... ....

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: If A = {v1, v2, ..., vn} be a basis for FV and n ≥ 2 then, is B = {v1+v2, , v2+v3, ..., vn+v1} also…

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Q: How are n, rank A, and nullity A related to each other how can one find a basis for Col A, Nul A,…

A: Write the relationship between n, rank A and nullity A. Also write a procedure to find a basis for…

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: Determine whether S is a basis for P3. S = {-3 + t³, 2t2, 2 + t, 1 + 2t + 2t2 + t3} O is a basis of…

A: A set S is a basis of a vector space V iff dimension of V= number of linearly independent vectors of…

Q: Explain why S is not a basis for P2.S = {−3 + 6x, 3x2, 1 − 2x − x2}

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Q: Find a basis for the null space of matrix A. [3 4 01 A = 1 2 1 Basis is

A: Let's find.

Q: 4 Let the basis for W is -5 -1 then the orthonormal basis for W is 3 а) 1 3/2 1 3/2 1 b) 3/2 3/2 3…

A: . Now, we need to find the orthonormal basis for W.

Q: 1- The vectors x, = (2,1, –4), x2 = (-3,4,1) and x3 = (2, –1,3) %3D %3D in R3, are A: represent a…

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Q: Let fi = 1+æ + 2x?, f2 = 2 + 3x + 3x?, f3 = 3 + 5x + 3x? and set F = (f1, f2, fs), a a13 a12 а11 a21…

A: We have to find transition matrix from S to F.

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

A: Basis definition:

Q: 1. Show that the following is a basis for R4:

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Q: Determine if S is a basis of P3. S = {1-t, 2t + 3t2, t2 - 2t3, 2+t3}

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Q: 3 4 If a basis for R3 is B and given [*]B find i in the standard basis. =

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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: If b1, b2 form an orthonormal basis for C and x is any vector in C, then O x4- x bị x b2 0 O x+ x bị…

A: We will find out the required value.

Q: Let M = {l; :C %3D Then M is not a basis for M because M is lincarly dependent the above is true…

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

A: Given a set S={1-x, 1-x2, -1-4x+5x2}  To Explain why S is not a basis for P2.

Q: Please give correct answer

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Q: Let B = {1+x, 1 – x², x + 2x²} and p(x) = 7+ 10x + 11x². You are given that B is a basis for IP2.…

A: NOTE: Refresh your page if you can't see any equations. . write all polynomial as a vector

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: Determine whether S is a basis for P3. S = {8 - t, t3, 7t2, 2t + t, -1 + 8t} Os is a basis of P3. O…

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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 M, 2. 1 0 0 1 Os is linearly dependent. O s does not span…

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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: Let S = {2x, 1 - x, x2 + x-1,x + 1, x - 2}. Then P1 OSis a basis for the above None of these P3 P2…

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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: Determine whether S is a basis for P3. S = {5 – t, t³, 4t2, 2t + t³, =1 + 5t} O is a basis of P3. O…

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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: 1 1 11

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Q: 4 Let the basis for W is -5 -1 then the orthonormal basis for W is 1 2 3 a) 1 3/2 3/2 1 3 b) 3/2 3/2…

A: Othonarmal basis for the given basis, using Gram-schmidt Ortho normal basics form

Q: Prove that if S= {v1, V2,..., Vn} is a basis for V and c is a nonzero constant, then S {cV1; cV2,…

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Q: Determine whether S is a basis for P3. S = {5 – 3t2 + t3, -2 + t2, 3t + t³, 5t} O is a basis of P3.…

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Q: Determine whether S is a basis for P3. S = {4 – 2t2 + t, -4 + t2, 3t + t2, 6t} O is a basis of P3. O…

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Q: Determine whether S is a basis for P3. S = {3 – 2t2 + t3, -2 + t², 3t + t³, 5t} S is a basis of P3.…

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Q: S {1-X,1+ X,1+X2, 1}. Then S is a P1 basis for None of these P2 P4 not a basis for basis for

A: This question is related to Linear Algebra

Q: is linearly independent. spans R3 5 is a basis for R³. None of the above.

A: Given set of vectors are : S=003.1,-2.74.90,-2.74.93.1 in R3 Now need to select which statements are…

Q: Which of the following is true? 0. 1 0 O A. is a basis for M22. O B. is a basis for M22. 1 0. 0. 0.…

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Q: Determine whether S is a basis for P3. S = {2 – t, t³, 7², 8t + t³, -1 + 2t} S is a basis of P3. S…

A: It is to be checked whether S is a basis of P3 or not where  S=2-t, t3, 7t2, 8t+t3, -1+2t

Q: -{圈[} B O B is an orthonormal basis for R?. O B is an orthogonal basis for IR?, but it is not…

A: Given B=1/21/2,1/2-1/2

Q: Determine whether S is a basis for P,. S = {-3 + t, 2t?, 3 + t, 3 + 2t + 2t2 + t°} O is a basis of…

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Q: 2. Let S ={2 , 1 in M31. a. Determine whether S spans M31. b. Determine whether S is linearly…

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Q: Determine whether S is a basis for P3. S = {6 – 2t2 + t³, -4 + t2, 3t + t³, 5t} O sis a basis of P3.…

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Q: If b1,b2 form an orthonormal basis for C² and x is any vector in C², then |x4 — 2 |x · b₁|²|x · b₂|²…

A: As per the question we are given the orthonormal basis b1 , b2 ∈ C2 and x is any vector in C2 Now…

Q: 1- The vectors x, = (2,1, -4), x2 = (-3,4,1) and x3 = (2, –1,3) in R3, are %3D A: represent a basis…

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Q: Let S = {1+4x– x², 2+5x+3x², 3x –5x², 3+15x +8x} . Does S span P,? Is S a basis for P, ? If not,…

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Q: Determine whether S is a basis for P S = {5 - 4t2 + t, -4 + t2, 2t + t, 5t} O is a basis of P2. O s…

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Q: Consider the limear thans femartin IC) - Ax de fiva by te matrix Ac 20 23 1 34 2 2 2. 1 20 D Find a…

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