Explain why S is not a basis for P,. S = {1 – x, 1 – x², -1 – 6x + 7x²} O sis linearly dependent. O s does not span P2: O 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: 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: Consider the following two ordered bases of R³: B C = a. Find the change of basis matrix from the…

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Q: Explain why S is not a basis for P2. S = {1, 4x, -6 + x², 7x} O sis linearly dependent. O s does not…

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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: 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 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 P2. S = {1, 4x, -9 + x², 7x} S is linearly dependent. O s does not…

A: Given S={1,4x,-9+x2,7x}. We explain why S is not a basis for P2.

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: 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 = {(-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 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 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 R3.S = {(0, 0, 0), (1, 0, 0), (0, 1, 0)}

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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: {( a + b+c+d b – c+ 2d а + 2с — d H = : a, b, c, d e R } C R³, and consider --(}) u = 1 (а) Is u E…

A: Given, H=a+b+c+db-c+2da+2c-d: a,b,c,d∈ℝ⊆ℝ3      ⋯⋯(1) a) Given, u=111 Consider the system,…

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: In Exercise, find the orthogonal complement W1 of W and give a basis for W1.

A: w=xy:3x+4y=0

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 P,. S = {1 – x, 1 – x², –1 – 6x + 7x²} 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: Explain why S is not a basis for R2.S = {(1, 2), (1, 0), (0, 1)}

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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: Find the orthogonal complement W⊥ of W and give a basis for W ⊥

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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: 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: 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: (a) Show that {v1, v2, V3} are linearly independent, where 1 V1 = 1 and v2 = and v3 = -2 Hence {v1,…

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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 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 - {(-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.…

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Q: Which of the following is a basis for the vector space R3?

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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 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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