16.-Linear-Algebra-by-Kenneth-Hoffman · Problem 1.3.6

Systems of Linear Equations

Mathematics — Linear Algebra · row-reduced-matrices

Problem

Let

A = \begin{bmatrix} a & b \\ c & d \end{bmatrix}

be a

2 \times 2

matrix with complex entries. Suppose that

A

is row-reduced and also that

a + b + c + d = 0

. Prove that there are exactly three such matrices.