Quote:

The linear system in x,y:

$\displaystyle (1+\lambda)x-\mu y=\delta$

$\displaystyle (1-\lambda)x+ \mu y=2$

has a unique solution precisely when:

a). $\displaystyle \lambda=\pm \mu \delta$

b). $\displaystyle \mu \neq \delta$

c). $\displaystyle \lambda \mu =2\delta$

d). $\displaystyle \mu \neq \delta$

What I did: Quote:

Let $\displaystyle T_1, T_2, T _3 : \Re^3 \rightarrow \Re ^2$ be given by:

$\displaystyle T_1(x,y,z)=(x+1,y+z),$

$\displaystyle T_2(x,y,z)=(2x,y)$

$\displaystyle T_3(x,y,z)=(x^2,y+z)$

which of $\displaystyle T_1,T_2$ and $\displaystyle T_3$ is a linear transformation?

a). $\displaystyle T_1$

b). $\displaystyle T_2$

c). $\displaystyle T_3$

d). none of them

I know that for a transformation to be linear: