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# Reduced Row Echelon Form of 2x2 Matrices

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(a) Show that if ad = bc &#8800; 0 then the reduced row echelon form of
[a b] is [1 0]
[c d] [0 1]

Assume that a &#8800; 0.
(b) Use your answer to part (a) to show that the linear system
ax + by = k
cx + dy = l
has exactly one solution when ad - bc &#8800; 0.
(c) If ad - bc = 0, under what conditions will the system have a solution? When will there
be no solution?

##### Solution Summary

The Reduced Row Echelon Form of 2x2 Matrices is investigated. The solution is detailed and well presented.

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