Please help me with these practice questions with steps and explaination to solve them. I am completely lost and struggling with these questions. please and thank you.

Question 4. In each case, illustrate the effect of the linear transformation on the unit square in R2 by a sketch similar to those in tables 7-10, Section 4.9. (So you should show what happens to the three corners of the square e1 , e2, and e1 + e2 .) N (a) T has standard matrix (b) T is a shear in the x direction by a factor of 2 followed by reflection through the line y = x . Question 5. For the matrix X = 3 4 find the eigenvalues and an eigenvector corresponding to each.Question 6. 0 1 2 (a) The matrix Y = 0 0 4 has 0 as its only eigenvalue. 0 0 Find the general solution to the problem of finding the corresponding eigenvectors. 2 (b) The matrix Z = 0 1 2 has 1 as its only eigenvalue. 0 0 1 Find the general solution to the problem of finding the corresponding eigenvectors. 4 8 O Question 7. For the matrix A = 0 find all the eigenvalues and for each 0 0 2 eigenvalue the general solution to the eigenvector problem. Question 8. k * 0 is an eigenvalue with corresponding eigenvector (1, 2, 3) of atb -2 A = 2 a -3 -6 b Find a, b, k.Question 3. Suppose that T : R2 > R3 is a linear transformation and T(1,1)=(4,7, 13) T(2,1)=(1, 1, 2) Find the standard matrix for T and use it to calculate T(1, 2) . Hint: The matrix is an unknown quantity with six unknown entries