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Unformatted text preview: 1 1 1 . Find a basis for S ⊥ . 3. The vector •4 7 ‚ has components 5 and3 with respect to the basis ‰• 1 2 ‚ , • 3 1 ‚± . What are the components of the vector •4 7 ‚ with respect to the basis ‰• 1 ‚ , • 11 ‚± of IR 2 ? 4. (a) Suppose A ∈ IR 19 × 48 8 , i.e., A is the coeﬃcient matrix of a system of 19 equations in 48 unknowns but only 8 of the equations are independent. How many linearly independent solutions can be found to the homogeneous linear system Ax = 0? (b) For the same A as in (a), how many linear independent solutions can be found to the homogeneous linear system A T y = 0?...
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 Spring '08
 lee
 Math, Linear Algebra, Linear Independence, Vector Space, Alan J. Laub, Prof. Alan J. Laub

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