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MATH 133 Lecture Notes - Elementary Matrix, Identity Matrix, Invertible Matrix

Mathematics & Statistics (Sci)
Course Code
MATH 133
Djivede Kelome

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Math 133
Elementary matrices
A nxn elementary matrix is a matrix obtained by performing a
single elementary row operation ont he nxn identity matrix (In)
Note that E is obtained by exchanging R and
R starting with
E is obtained by multiplying R by 5 starting with
A is not an elementary matrix

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let A be a nxm matrix!
Performing a single row operation on A is equivalent to multiplying
A from the left by an elementary matrix.
E; Eis obtained by performing the same row operation
Theorem: if E is an elementary matrix then E is invertible and actually
E is also an elementary matrix.
Suppose that E is obtained from by exchanging R and R
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