Suppose V is a subspace of R" and suppose {v1, v2, v3} is a basis of V. Decide if the following sets of vectors are a basis for V: (i) {v2, v1 – 5v3, 2v3} (ii) {v2, v1 – 5v3, 2v3, 302 + 7v3 – v1} (iii) {2v2 – v3, V1}

Q: 2. How many vectors does any basis of of Max(a+2)(R) contain, if a = max1<i<10 a;?

A: Since, dimension of a vector space is equal to number of elements in basis of vector space.

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A: From part ii)We have to show that the set  is a basis of .We know thatA basis B of a vector space V…

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A: The solution are next step

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A: Let V be the vector space Since v1,v2,v3,v4 span the vector space V.

Q: 3) Let C be a basis that contains vectors (1 + (-1) x + 1x² + 1x³), (1 + 2x + 2x² + (−1) x³), (1 +…

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A: The given vectors  and .The objective is to find the orthogonal complement of the given vectors.

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A: Given that w=0828-31v1=1-210v2=-1308v3=1-4-53

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Q: ) Consider the vectors -- () --- () --- () a= = Do these vectors form a basis of R³? If yes, prove…

A: Please comment if you need any clarification. If you find my answer useful please put thumbs up.…

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A: 1) Let Tabcd=0a+0b+0c+4d1a+(-1)b+(-2)c+4d0a+1b+(-2)c+5d1a+(-1)b+(-2)c+2d2a+1b+(-10)c+4d   To Find:…

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A: this a spanning set and linearly independent so the vectors forms a basis of R^2

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Q: 1 ): The vectors 2 and form a basis the vector space R'. Select one: O True O False

A: Here we state whether it is true or false.