Explain why S is not a basis for R2. S = {(2, 5), (8, 20)} O Sis linearly dependent. O s does not span R2. O sis linearly dependent and does not span R2.

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 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 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 – 4x + 5x2} O sis linearly dependent. O…

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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 R². S = {(-6, 2)} OS is linearly dependent. S does not span R². OS…

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

A: Solution

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

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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 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 i not a basis for R?. S= {(5, 3), (1, 0), (0, 1)} O sis linearly dependent. O s does…

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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 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.

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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: Note: For R 2 the span should be 2. And the two vectors should be linearly independent.

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 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 P2. S = {1 - x, 1 – x4, –1 – 2x + 3x2} O S is linearly dependent. O…

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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 P2. S = {1 – x, 1 – x², –1 – 3x + 4x²} 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 = {(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: 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 – 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 R2. S = {(-6, 6)} O sis linearly dependent. S does not span R². S…

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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 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 i not a basis for P2. s = {1 - x, 1 - x2, -1 – 2x + 3x?} O is linearly dependent. O s…

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Q: Consider the set S: Is this set a basis for R2? Why or why not? What can be said about how can be…

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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 R2. S = {(-2, 6), (0, 0)} O is linearly dependent. O s does not…

A: Given : S=-2,6,0,0   To Find : Why S is not basis of R2

Q: Determine whether or not W1 and W2 are: A) not a basis because it does not span R^3 B) not a basis…

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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 R. S = {(0, 1, 0), (0, 0, 0), (0, 0, 1)} Os is linearly dependent.…

A: Given : S={(0,1,0),(0,0,0),(0,0,1)}

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 = {(-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 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 R². S = {(1, 5), (1, 0), (0, 1)} O s is linearly dependent. O s…

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

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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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