2331_Notes_2o3_fill - Math 2331 Linear Algebra Section 2.3...

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Math 2331 Linear Algebra Section 2.3 and 2.4 Multiplying Matrices and Elimination Example Suppose 100 310 001 E =− ⎜⎟ and 13 2 31 3 42 2 A ⎛⎞ ⎝⎠ Find EA Suppose 010 P = PA = Suppose 10 0 01 0 00 2 D = DA = Notice that all of our legal elimination moves may be accomplished by multiplying the matrix A on the left by a another matrix. You can prove to yourself that the matrices E, P and D are invertible!
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Let's Look at this more closely and with notation from the book: Elimination with Matrices Subtracting a Multiple of row j from row i ij E that subtracts a multiple K of row j from row i is the identity matrix with an extra nonzero entry -K in the (i,j) position in the matrix. 13 2 31 3 42 2 A ⎛⎞ ⎜⎟ =− ⎝⎠ Subtract 3 times row 1 from row 2 - Matrix - Result - Next (USING THE RESULT OF THE LAST OPERATION) Subtract 4 times row 1 from row 3 - Matrix- Result Continuing: For column 2 -
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2331_Notes_2o3_fill - Math 2331 Linear Algebra Section 2.3...

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