Explain why S is not a basis for P,. .2 S = (1 - x, 1 - x², -1 – 8x + 9x²} O s is linearly dependent. S does not span P, S is linearly dependent and does not span P,.

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: Determine whether S is a basis for P,. S = {5 – 4t2 + t°,-4 + t2, 2t + t, 5t) S is a basis of P3. O…

A: Find your answer below

Q: Explain why S is not a basis for R². s={(6, 8), (1, 0), (0, 1)) S is linearly dependent. OS does not…

A: We will use S to determine which among the given options is correct.

Q: Is B a basis for P2? B = {-x +1 ,2x +3, x² }

A: Given B =  -x+1 , 2x+3 , x2  We know that the standard basis of P2 is   1 , x , x2 .

Q: Explain why S is not a basis for P. S = {1, 8x, -4 +x², 9x} O sis linearly dependent. O s does not…

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

A: S=3-4t2+t3, -2+t2, 2t+t3,6t Consider , a3-4t2+t3+b-2+t2+c2t+t3+6td=0 ; a,b,c,d∈ℝ…

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 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 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 P2.S = {−3 + 6x, 3x2, 1 − 2x − x2}

A:

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: Let, a1, a2 and a3 are the basis for R. [R1] y = |R2 [R3] a1 = |0 a2 = |0 a3 = Find the following:…

A: Since you've asked multiple questions, as per our answering guidelines we are supposed to solve the…

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 P2.S = {2, x, 3 + x, 3x2}

A: From the given value for S to find the values for pi(x).

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

A: Consider a matrix formed by vectors of S and determine the determinant of the matrix, 1-1010-1-1-67=…

Q: . If {x1, X2, X3} is a basis of V3 (R), show that {x, +x2, X2 + x3, X3 + X1} _is also a basis of V3…

A: Given problem is :

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 M, O sis inearly dependent. O s does not span M.2 O sis linearly…

A: We can solve this as follows:

Q: 1

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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…

A:

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

A:

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 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 R2. S = {(-6, 4)} O sis linearly dependent. O s does not span R2. O…

A:

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

A:

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 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: 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: Determine whether S is a basis for P3. S= (3-t, t3, 9t2, 8t + t, -1 + 3t) OS is a basis of P3. OS is…

A: Please see the below picture for detailed solution.

Q: Let B = {x²+x,-2x² + 3x + 3, 2x² – x – 2} be a basis of P2(R)

A: Given,            B=x2+x,  -2x2+3x+3,  2x2-x-2

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: Explain why S is not a basis for R2. S - {(-5, 2)} O sis linearly dependent. O s does not span R2. O…

A: Basis :  The set of vectors v1,v2,...,vn ⊆V in a vector space V is called a basis for V if (i) S is…

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 S is linearly dependent. O s does not span R2.…

A:

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: 23. Suppose R* = Span {v1, ..., V4}. Explain why {v1,..., V4} is a basis for R4.

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

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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 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…

A: