# Math Help - Linear map

1. ## Linear map

Show that the linear map $T:\wp_2 \to \wp_2$ defined by $T(\alpha_0+\alpha_1 x+\alpha_2x^2)=(\alpha_0+\alpha_1)+(\alpha_1+2\alp ha_2)x+(\alpha_0+\alpha_1+3\alpha_2)x^2$ is non-singular and find its inverse.

Thanks in advance.

2. Have you learned on coordinate-vectors?
Choose the base: {x^2, x, 1} ... Find the coordinate-vector of the image of this map, find its determinant and continue from there...