2. (3 points) Consider the following transformation from R4 - R3: TA(X1, X2, X3, X4) = (X1 + 2x2 -4X3, *1 - 5x3, X2 + 6X4) Show that TA can be represented as matrix multiplication and find a basis for the kernal (TA) and the Range (TA). 3. (3 points) Consider the following transformation from R3 - R3: TA(X1, X2, X3,) = (x1 - 2x2 + 2x3, 2x1 + X2 + X3,X1 + X2) Represent T as matrix multiplication. Determine if T is one to one and invertible. If yes, find the matrix of the transformation and a formula for TA-1. If not explain why. O 4. (4 points) For the matrix A = , find the following: 1 0. a. The characteristic equation of A b. The eigenvalues of A c. The eigenvectors associated with each eigenvalue d. Show that each eigenvalue/ eigenvector combination works by showing Ax = 1x