C3093314 - 14(Statement of the problem Solution Consider...

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14. (Statement of the problem.) Solution. Consider the equation A x = 0 . (1) If we denote by a 1 , · · · , a n the column vectors, and denote x = ( x 1 , · · · , x n ) T , then (1) can be written as x 1 a 1 + · · · + x n a n = 0 . Since a 1 , · · · , a n are linearly independent, this equation implies
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Unformatted text preview: x 1 = ··· = x n = 0. Hence, is the only solution to (1). It follows by the definiton that N ( A ) = { } . / 1...
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