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Unformatted text preview: . 2) (5 points) Let B = 1 2 25 1 2 37246 14 . Compute rank( B ) and dim Nul( B ). In order to compute rank( B ), we must identify the number of pivot columns of B . Thus, we begin by row reducing: 1 2 25 1 2 37246 14 R 2 ← R 2R 1→ 1 2 25 12246 14 R 3 ← R 3 +2 R 1→ 1 2 25 0 0 12 0 02 4 R 3 ← R 3 +2 R 2→ 1 2 25 0 0 12 0 0 0 . From this row echelon form, we can identify that the matrix has 2 pivot columns. Thus, rank( B ) = 2. Now, using the identity that for an m × n matrix, n = rank( B ) + dim Nul( B ), in this case, we have dim Nul( B ) = 42 = 2....
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This note was uploaded on 03/17/2011 for the course MATH 20F taught by Professor Buss during the Winter '03 term at UCSD.
 Winter '03
 BUSS
 Math, Linear Algebra, Algebra

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