Explain why S is not a basis for P2. S = {1 - x, 1 – x4, –1 – 2x + 3x2} O S is linearly dependent. O s does not span P2. OS is linearly dependent and does not span P2.

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: 4 Let A = and define T : R? → R? by T(x) = Ax. Find a -2 -1 basis B such that the matrix [T]s is…

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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: 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 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, 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: 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: (e) Explain that Sį is a basis for R3 and that S2 is not. (f) Determine the coordinates of X1 U =…

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Q: Explain why S is not a basis for P2. S = {1, 6x, –7 + x2, 9x} O Sis linearly dependent. O s does not…

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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: Let p1(t) = t and p2(t) = t + 1 be polynomials in P3. (a) Show that p1(t) and p2(t)} are linearly…

A: Given: p1t=tp2t=t+1 (a) We have to show that p1t and p2t is linearly independent. (b) We have to…

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=…

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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 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: Explain why S is not a basis for R2. S = {(4, 3), (8, 6)} O is linearly dependent. O s does not span…

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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 P2. S = {1, 6x, –9 + x², 7x} 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), (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, 2), (o, 0)} O sis linearly dependent. S does not span…

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

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Q: Explain why S is not a basis for R². S= {(6, 3), (18, 9)} O is linearly dependent. O s does not span…

A: Given that s={(6,3),(18,9)}

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, 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 P,. S = {1, 2x, -4 + x², 3x} S is linearly dependent. O does not…

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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 - {(-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.…

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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 = {(-3, 7), (0, 0)} O sis linearly dependent. O s does not…

A: Let V=v1,v2∈R2.

Q: Consider B find [p(x)]B. {x2 + x, 2 + 2x, 1} an ordered basis of P2(R). If p(x) = 4.x² 2x – 6, %3D

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Q: Explain why S is not a basis for R2. S = {(2, 5), (6, 15)} 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 – 7x + 8x²} O sis linearly dependent. O…

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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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