I have the following problem
Consider in $\mathbb{R}^2$ the set of points satisfying the equation $2x_2 − x_1 − 2 = 0$. Show on a plot the points satisfying this equation (you can use matlab for this). How are these points transformed by the following matrix: $$ \begin{bmatrix}2 & -1\\-1 & 1\end{bmatrix} $$ [Show the transformed set and plot it – you can use matlab again]
I could be mistaken but would the matrix be $$ \begin{bmatrix}2 & -1 -2\end{bmatrix}? $$
After that I am very stuck. Thanks
Let x2 = t then it follows that x1= 2t -2 Put these two t-expressions in a 2 by 1 matrix and perform matrix multiplication with the given matrix. You get a new 2 by 1 matrix with entries in terms of t. The first entry is your new x1 and the second entry is your new x2. Eliminate the t from it and you have a new equation in terms of x1 and x2 I would like you to try that out (and share with us if you wish) But a far easier approach would be the following: Realize that a line subject to your matrix is just another line (which you will come to see when you do my above method). So pick any two points on your given line and subject those points each to your matrix through a multiplication. You obtain two new points. You can then find the equation that passes through these points.