notes1-8 - SECTION 1.8 ANOTHER WAY TO THINK ABOUT A x = b A...

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Unformatted text preview: SECTION 1.8 ANOTHER WAY TO THINK ABOUT A x = b A x = b is a way to write a system of equations. Heres the new way to think about A x . Given a vector x , then A x is another vector y . When the matrix A is m n , then we get a function or transformation T from R n , called the domain of T , to R m . For a vector x in R n , the vector T ( x ) = A x is the image of x . Finally, the set of all images T ( x ) is called the range of T . EXAMPLE. Suppose that A = 1- 2 1 3- 4 5 1 1- 3 5- 4 and b = 1 9 3- 6 . Define the transfor- mation T as above by T ( x ) = A x . Is b in the range of T ? If so, find a vector x whose image under T is b and determine whether x is unique. The algebra of matrix-vector multiplication is fairly nice. In particular, A ( u + v ) = A u + A v and A ( c u ) = cA u . We can translate this nice algebra into properties of the transformation T : A function or transformation from R...
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This note was uploaded on 05/07/2010 for the course M 56945 taught by Professor Danielallcock during the Spring '09 term at University of Texas at Austin.

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notes1-8 - SECTION 1.8 ANOTHER WAY TO THINK ABOUT A x = b A...

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