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Determine if each of the following sets of vectors U is a subspace of the specified...

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Advance Math

Determine if each of the following sets of vectors U is asubspace of the specified vector space, and if so, describe the setgeometrically:

  1. (a) U ? R2, where U = {?x1,x2? : x1 = 0}

  2. (b) U ? R2, where U = {?x1,x2? : x1x2 = 0}

  3. (c) U?R3,whereU={?x1,x2,x3?:?1,2,3?·?x1,x2,x3?=0}

  4. (d) U ? R3, where U = {?x1,x2,x3? : ?1,2,2? · ?x1,x2,x3? = 0and

    ?1, 3, 0? · ?x1, x2, x3? = 0}

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