If you find any mistakes, please make a comment! Thank you.

Find all solutions to the systems of equations by row-reducing (1)


Solution to Linear Algebra Hoffman & Kunze Chapter 1.3 Exercise 1.3.1

Solution: The matrix of coefficients is
$$\left[\begin{array}{cc}1-i&-i\\2&1-i\end{array}\right].$$Row reducing
$$\rightarrow \left[\begin{array}{cc}2&1-i\\1-i&-i\end{array}\right]\rightarrow\left[\begin{array}{cc}2&1-i\\0&0\end{array}\right]
$$Thus $2x_1+(1-i)x_2=0$. Thus for any $x_2\in\mathbb C$, $(\frac12(i-1)x_2,x_2)$ is a solution and these are all solutions.


Linearity

This website is supposed to help you study Linear Algebras. Please only read these solutions after thinking about the problems carefully. Do not just copy these solutions.
Close Menu