Consider the (2 × 2) system a11 + a12 x1 = b1 a21 x1 + a22
Chapter 1, Problem 37E(choose chapter or problem)
Problem 37E
Consider the (2 × 2) system a11 + a12 x1 = b1 a21 x1 + a22 x2 = b2 Show that if a11a22 – a12a21 ≠ 0, then this system is equivalent to a system of the form c11x1 + c1 x2 = d1 c22 x2 = d2 where c11 ≠ 0 and c22 ≠ 0. Note that the second system always has a solution. [Hint: First suppose that a11 ≠ 0, and then consider the special case in which a11 = 0.]
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