Worksheet4 - Worksheet 4 February 2nd, 2009 1. If Ax = Ay...

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Worksheet 4 February 2nd, 2009 1. If A x = A y must x = y ? If so explain why, if not, find an A and two vectors x 6 = y such that A x = A y 2. Construct two 3 × 3 matrices A and B such that AB = 0, A 6 = 0, B 6 = 0, and BA 6 = 0. 3. Suppose for T : R n R n that T ( x ) = b and T ( y ) = b for some x 6 = y , can T map R n onto R n . 4. We know we can write any function f : R 2 R 2 as f ( x,y ) = ( f 1 ( x,y ) ,f 2 ( x,y )). Consider the linear transformation f ( x ) = A x where A = ± 3 4 2 - 1 ² . Write this function as f ( x,y ) = ( f 1 ( x,y ) ,f 2 ( x,y )). 5. Matrix multiplication is not necessarily commutative.
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This note was uploaded on 04/02/2009 for the course MATH 54 taught by Professor Chorin during the Spring '08 term at University of California, Berkeley.

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