Explain why S is not a basis for P₂. S = {1, 6x, -2 + x²,4x} O S is linearly dependent. OS 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, 2)}

A: We know the definition of basis, let V be a vector space. Let B be a set of vectors in vector space…

Q: Explain why S is not a basis for P,. S = {1, 3x, -4 + x2, 6x} O sis linearly dependent. s does not…

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

A: Given: S=-6, 4. We have to explain why S is not a basis for R2.

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: Explain why S is not a basis for R2.S = {(6, −5), (12, −10)}

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Q: Explain why S is not a basis for P₂. S = {1x, 1x², −1 − 5x + 6x²} OS is linearly dependent. OS does…

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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 – 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 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, 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 = {(2, 5), (6, 15)} O sis linearly dependent. O S does not…

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