# Previous answers holtlinalg1 42042 determine if the

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18. 1/1 points | Previous Answers HoltLinAlg1 4.2.042. Determine if the statement is true or false, and justify your answer. If then S = span{ u 1 , u 2 , u 3 }, dim( S ) = 3. True, by the defintion of the dimension of a subspace. False. For example, if S = span , , , then dim( S ) < 3. 1 0 0 1 1 0 0 1 1 0 1 1 1 1 ,
19. 1/1 points | Previous Answers HoltLinAlg1 4.2.043. Determine if the statement is true or false, and justify your answer. If a set of vectors U spans a subspace S , then vectors can be added to U to create a basis for True, by the theorem that says let U = { u 1 , ..., u m } be set of vectors in a subspace S { 0 } of R n . If U spans S , then additional vectors can be added to U to form a basis of 1 0 0 1 1 1 S . S .
False. For example, if then U spans but adding additional vectors False. For example, if U = , , then U spans S = R 2 , but adding additional vectors will not yield a basis. 0 0 1 1 1 1 2 2 , R
will not yield a basis.
20. 1/1 points | Previous Answers HoltLinAlg1 4.2.044. Determine if the statement is true or false, and justify your answer. If a set of vectors U is linearly independent in a subspace S , then vectors can be added to U create a basis for S to . S 1 0 0 1 S S S , ,