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Unformatted text preview: 4. Compressing photo images (gif, jpeg) 5. MP3 (I think) FACT. If T is a linear transformation, then 1. T ( ) = , and 2. T ( c 1 v 1 + c 2 v 2 + ··· + c p v p ) = c 1 T ( v 1 ) + c 2 T ( v 2 ) + ··· + c p T ( v p ) . In engineering Fact 2 is called the superposition principle. Example. Find all x in R 4 that are mapped into the zero vector by the linear transformation x → A x for the matrix A = 12 1 0 34 5 2 1 1 13 54 1 . Example. When u and v are LI vectors in R n , then the plane P through u , v , and has parametric equation x = s u + t v . Show that a linear transformation T from R n to R m maps P onto a plane, or a line, or just the origin. HOMEWORK: SECTION 1.8...
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 Spring '08
 PAVLOVIC
 Linear Algebra, Algebra, Equations, Vector Space, ax

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