# Reduced Row Echelon Form of 2x2 Matrices

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(a) Show that if ad = bc ≠ 0 then the reduced row echelon form of

[a b] is [1 0]

[c d] [0 1]

Assume that a ≠ 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 ≠ 0.

(c) If ad - bc = 0, under what conditions will the system have a solution? When will there

be no solution?

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

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