20 11 points previous answers holtlinalg1 41058

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20. 1/1 points | Previous Answers HoltLinAlg1 4.1.058. 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 Since S is a subspace, both and belong to S , and hence belongs to True. 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, both (1 s ) u and s v belong to S , and hence (1 s ) u belongs to S True. 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 belongs to 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 (1 s ) u belongs to S , and hence (1 s ) u does not belong to 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, neither (1 s ) u nor s v belong to S , and hence (1 s ) u + s v does not belong to 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 not belong to S S . s . S . + s v . . + s v . S . v does . v s v
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 = ( 7 , 6 , 4 , 1) null( A ). a a 4 = $$ 7 a 1+6 a 2 4 a 3 4 , 0 . .

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