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[Solution] Let P be a vector space generated by the set: S=(0,1,1),(1,2,3),(3,-1,2) and Q be the vector space generated by T=(1,1,0),(0,1,1) Is S a basis

Question: Let P be a vector space generated by the set:

\[S=\{\left( 0,1,1 \right),\left( 1,2,3 \right),\left( 3,-1,2 \right)\}\]

and Q be the vector space generated by

\[T=\{\left( 1,1,0 \right),\left( 0,1,1 \right)\}\]

Is S a basis for P ? If not, construct a basis.

Is T a basis for Q ? If not, construct a basis.

Find the intersection of P and Q . Is the intersection a vector space?

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[Solution] Let P be a vector space generated by the set: S=(0,1,1),(1,2,3),(3,-1,2) and Q be the vector space generated by T=(1,1,0),(0,1,1) Is S a basis

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