Transcription of 3Elementary row operations and their …
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3Elementary row operations and their …
3 elementary row operations and their correspondingmatricesAs we ll see, any elementary row operation can be performed by multiplying the augmentedmatrix (A|y) on theleftby what we ll call anelementary matrix. Just so this doesn tcome as a total shock, let s look at some simple matrix operations : SupposeEAis defined, and suppose the first row ofEis (1,0,0, .. ,0). Then the firstrow ofEAisidenticalto the first row ofA. Similarly, if theithrow ofEis all zeros except for a 1 in theithslot, then theithrowof the productEAis identical to theithrow ofA. It follows that if we want tochange onlyrow i of the matrixA, we should multiplyAon the left by some matrixEwith the following property:Every rowexceptrow i should be theithrow of the corresponding identity procedure that we illustrate below is used to reduceanymatrix to echelon form (notjust augmented matrices ).
3Elementary row operations and their corresponding matrices As we’ll see, any elementary row operation can be performed by multiplying the augmented
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