$$Right or Wrong $(2$ points each, $10$ points total$)$

$$

Vectors $(1,2,3{)}^T$ and $(6,7,8{)}^T$ are linearly independent.

The mapping $L$:$R^3{R}^2$ defined by $L(x)=(1+x_1,-x_2)$ is a linear transformation.

The subset $\{(x_1,x_2,x_3{)}^T|x_1=x_2+x_3\}$ of $R^3$ is a subspace.

Vectors $(1,0{)}^T$ and $(0,1{)}^T$ form a basis of $R^2.$

The matrix $([0,1],[0,0])$ does not have a multiplicative inverse.