- #1
Buffu
- 849
- 146
Homework Statement
Let ##A = \begin{bmatrix} a&b\\c&d \end{bmatrix}## such that ##a+b+c+d = 0##. Suppose A is a row reduced. Prove that there are exactly three such matrices.
Homework Equations
The Attempt at a Solution
1) ##\begin{bmatrix} 0&0\\0&0 \end{bmatrix}##
2) ##\begin{bmatrix} c&0\\0&-c \end{bmatrix}##
3) ##\begin{bmatrix} c&-c\\0&0 \end{bmatrix}##
4) ##\begin{bmatrix} 0&0\\c&-c \end{bmatrix}##
5) ##\begin{bmatrix} 0&c\\-c&0 \end{bmatrix}##
Where ##c \in \Bbb C##.
Is the question incorrect ?
Last edited by a moderator: