# 235_midterm_s15_soln - Math 235 Midterm Solutions 1 Short...

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Math 235Midterm Solutions1.Short Answer Problems[1](a) State the definition of the row space of anm×nmatrixA.
(b) State the definition of the rank of a linear mappingL:VW.
(c) LetB={~v1,~v2}be a basis for a vector spaceVand letL:VVbe a linearmapping. If [L]B=13-21and [~x]B=12, then what isL(~x)?
(d) LetAbe anm×nmatrix andBbe an×mmatrix. Prove that ifAB= 0, thenCol(B)Null(A)
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[5]2.Find a basis for the four fundamental subspaces ofA=-123852-3-41101.
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[3]3.(a) State the definition of an inner producth,ion a vector spaceV.