C__DOCUME~1_MAXWID~1_LOCALS~1_Temp_plugtmp-27_notes2-1

C__DOCUME~1_MAXWID~1_LOCALS~1_Temp_plugtmp-27_notes2-1 - ,...

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SECTION 2.1 MATRIX ALGEBRA You can multiply matrices by scalars (numbers); when two matrices are the same size you can add and subtract them; when two matrices are appropriate sizes you can multiply them. The algebra is nice [Theorem 1, page 108; Theorem 2, page 113], EXCEPT that matrix multiplication is not commutative, that is, AB may not equal BA even when both are defined. And you have to be a little careful about the sizes. For each positive integer m there is an m × m matrix I m , called an identity matrix , such that I m A = A and BI m = B whenever the products are defined. If we interchange the rows and columns of an m × n matrix A , we get an n × m ma- trix A T
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Unformatted text preview: , called the transpose of A . Transposes preserve scalar multiplication and addi-tion/subtraction, but reverse multiplication [Theorem 3, page 115]. EXAMPLE. Suppose that A = " 1-2 1 3-4 5 # and B = 1 9-2 3 1 . Compute 2 A +3 B T , AB , BA , and B T A T . HOMEWORK: SECTION 2.1 EXAMPLES, IF TIME. Suppose the third column of B is the sum of the rst two columns of B . What can you say about the third column of AB ? Why? Suppose CA = I n . Show that the equation A x = has only the trivial solution. Explain why A cannot have more columns than rows....
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This note was uploaded on 04/15/2008 for the course M 340L taught by Professor Pavlovic during the Spring '08 term at University of Texas at Austin.

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C__DOCUME~1_MAXWID~1_LOCALS~1_Temp_plugtmp-27_notes2-1 - ,...

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