# Determine if the statement is true or false and

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Determine if the statement is true or false, and justify your answer. If u and v are in a subspace S , then every point on the line connecting u and v is also in T : R 2 R 7 range( T ) R 2 True, by the theorem that says let T : R m R n be a linear transformation. Then the range of is a subspace of R m False, because range( T ) is a subspace of R 7 False, because range( T ) is a subspace of R 5 False, because range( T ) is a subspace of R False, because range( T ) is a subspace of R 9 True. Every point on the line connecting u and v is of the form (1 s ) u + s v for some scalar Since S is a subspace, then only s v belongs to S , and hence (1 s ) u + s v belongs to True. Every point on the line connecting u and v is of the form (1 s ) u + s v for some scalar Since S is a subspace, both (1 s ) u and s v belong to S , and hence (1 s ) u + s v belongs to S . S . . T . . . . . s . S . s . .
False. Every point on the line connecting u and v is of the form (1 s ) u + s v for some scalar s . Since S is a subspace, then only s v belongs to S , and hence (1 s ) u + s v does not belong to S . v does .
21. 2/2 points | Previous Answers HoltLinAlg1 4.1.068. Let and suppose that is in Write as a linear combination of the other three vectors. A = [ a 1 a 2 a 3 a 4 ], x = ( 9 , 3 , 4 , 1) null( A ). a a 4 = 4