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Homework set 
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(mostly from Martin Brown,
"Differential Equations and Their Applications", 4th edition)
For systems of linear equations and other matrix computations
(inverses, determinants) larger than 2x2,
use the corresponding augmented matrix
and apply the Gauss-Jordan elimination method
(sequence of elementary row operations)
to reduce this matrix to reduced row echelon form.
Do all computations by hand, but you can check e.g. with this
online calculator.