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Unformatted text preview: i th entry oF the row with the i th entry oF the column, multiply each matched pair, and add: b a 1 a 2 a 3 B x 1 x 2 x 3 = a 1 x 1 + a 2 x 2 + a 3 x 3 . OF course, in this language, we are representing the linear Function ℓ : R 3 → R as the product oF its matrix representative with the coordinate matrix oF the input ℓ ( −→ x ) = [ ℓ ][ −→ x ] . Another way to think oF this representation is to associate, to any row , a vector −→ a (just put commas between the entries oF the row matrix), and then to notice that the product oF the row with the coordinate matrix oF −→ x is the same as the dot product oF the vector −→ a with −→ x : b a 1 a 2 a 3 B x 1 x 2 x 3 = ( a 1 ,a 2 ,a 3 ) · ( x 1 ,x 2 ,x 3 ) = −→ a · −→ x ....
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This note was uploaded on 10/20/2011 for the course MAC 2311 taught by Professor All during the Fall '08 term at University of Florida.
- Fall '08