Arrange your two windows so that you can move easily back-and-forth between them. This new window shows a vector x represented by a blue ball and the vector y = Ax, represented by a red ball, determined by applying the linear transformation represented by a matrix A to the vector x. You can change the vector x by dragging the blue ball. Notice as the vector x changes, so does the vector y = Ax. Your job is to determine the matrix A that defines this particular linear transformation. This is the first of a series of questions like this.
Click here to open another new window with another live figure that you can use to check your answers to these questions. Arrange your desktop so that you can move easily back-and-forth among all these windows. This new "working live figure" is similar to the live figure for Question 1 except it shows a different linear transformation and it also shows the matrix A that defines this linear transformation. You can change the entries in this matrix by editing them in the usual way. You can test your answer to question 1 (and to the later questions) by editing the matrix and seeing if behavior of the linear transformation you have defined in this new window matches the unknown linear transformation in the question window.
from the behavior of the linear transformation?