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 A and B are equivalent matrices, then row( A ) = row( B ). True, by the theorem that says if A and B are equivalent matrices, then the subspace spanned by the rows of A is the same as the subspace spanned by the rows of B . 10 01 11 00
Solution or Explanation True, by Theorem 4.10 , and the definition of row space. In particular, if B is an echelon form of A , then this is Theorem 4.20(a) . False. For example, if A = and B = , then A and B are equivalent matrices, but row( A ) row( B ). 10 01 01 10
12. 1/1 points | Previous Answers HoltLinAlg1 4.3.047. Determine if the statement is true or false, and justify your answer. If A and B are equivalent matrices, then Solution or Explanation False. For example, let col( A ) = col( B ). True, by the definition of column space. True, by the Big Theorem. False. For example, let A = and B = . 10 01 11 01 False. For example, let A = and B = . 10 00 10 10 False. For example, let A = and B = . 10 00 10 01 A = and B = . 1 0 0 0 1 0 1 0
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