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Unformatted text preview: A is at least 2. However, A has only two columns, so its rank is at most 2. Therefore, the rank of A is 2. Alternately, we could rowreduce A and see that the reduced form has 2 nonzero rows. 2. Find a number n such that the vectors h 1 , 2 , i , h , 2 , 3 i , and h 3 , 2 , n i are linearly dependent . Solution : Consider the matrix whose rows are the given vectors: 1 2 0 0 2 3 3 2 n . The row vectors are linearly dependent if and only if we can row reduce and obtain at least one row of zeros. Rowreducing: 1 2 0 0 2 3 3 2 n 1 2 2 34 n 1 2 0 2 3 0 0 n + 6 The reduced form of the matrix has a row of zeros if and only if n =6. Therefore, the given vectors are linearly dependent when n =6....
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 Spring '07
 Cremins
 Calculus, Linear Algebra, Algebra

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