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Unformatted text preview: A T ). (a) Show that b R and b N are unique. (b) Show that b T R b N = 0. (c) If b R and b N are both nonzero, show that they are linearly independent. Exercise 3.4. * Consider the matrix A and vector y given by A = 7-7-7 2 4 6 7 7 7 14 6 2-2 5 3 1 4 9 6 3 9 5 2-1 1 and y = -7-3 1-1 . (a) Find the rank of A . Use the Matlab command null to nd a basis for null( A ). (b) Find the unique vectors y R range( A T ) and y N null( A ) such that y = y R + y N . Exercise 3.5. Let A be an m n matrix with rank m . Use the unique decomposition of a vector into the sum of its null- and range-space portions to show that the system Ax = b is compatible for every b R m ....
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- Spring '08
- Linear Programming