Explain why S is not a basis for P2. S = {1, 2x, -5 + x², 9x} O sis linearly dependent. O s does not span P2. O s 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: Explain why S is not a basis for R2. S = {(-5, 8), (0, 0)} %D O sis linearly dependent. O s does not…

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

A: To find why S is not a basis for ℝ3 where S=(4,1,6),(13,6,8),(-5,1,3),(0,4,6)

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: 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 the set (a) spans R3, (b) is linearly independent, and (c) is a basis for R3.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= {(-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 R2. S = {(4, 3), (16, 12)} O s is linearly dependent. S does not…

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Q: Explain why S is not a basis for P2. S = {1, 2x, –4 + x², 3x} O sis linearly dependent. O s does not…

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

A: Let V=v1,v2∈R2. Now S=-3,7,0,0. A set of vectors S=v1,v2,⋯,vn in a vector space V is a basis for V…

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 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: 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: 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: 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 R2. S = {(-4, 8), (0, 0)} O is linearly dependent. O s does not…

A: Note: A linearly independent set S containing n vectors in Rn is a basis of Rn.  If S is a basis of…

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 = {(-4, 8), (0, 0)} O sis linearly dependent. O s does not…

A: S is not a basis for R2 because S is linearly dependent.

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 R3. S = {(1, -5, 3), (6, 13, 8), (1, 4, 6), (0, 5, 7)} O sis…

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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 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 i not a basis for R². S = {(-3, 7)} O sis linearly dependent. O s does not span R2. O…

A: We will find out the required solution.

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 R2. S = {(-3, 4)} S is linearly dependent. S does not span R2. O…

A: The set S=-3,4 is not a basis for R2.

Q: Explain why S is not a basis for R2. S = {(3, 6), (1, 0), (0, 1)} O sis linearly dependent. O s does…

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Q: Explain why S is not a basis for R. S = {(6, 8, 13), (1, 3, -5), (1, 6, 4), (0, 8, 7)} S is linearly…

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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 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 = {(5, 2), (1, 0), (0, 1)} O Sis linearly dependent. S does…

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

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: 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 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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