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Lecture

School

McGill UniversityDepartment

Mathematics & Statistics (Sci)Course Code

MATH 133Professor

Djivede KelomeThis

**preview**shows pages 1-2. to view the full**6 pages of the document.**Math 133

Exercise:

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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Theorem:!

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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