2. For the 2x2 matrices, what is the set of matrices which commute with every matrix with exactly two entries equal to one and the other entries equal to zero.
3. What is the dimension of the range of the linear operator T: 2x2matrices to 2x2matrices defined by T(A)=AB-BA, if B is all zeros except for the (i,j)th entry in which there is a 1? Give a complete explanation.
Assignment 2.
259/11,15,17
Let A be the nxn matrix with 1's (on the diagonal) just above the main diagonal and 0's everywhere else. Find all the powers, A^n, of the matrix, A. (That is, the product of A with itself any number of times.)
Let B be any fixed 2x2 matrix. Describe the set of 2x2 matrices which commute with the fixed matrix, B.
Consider the set W of 2x2 matrices with a_{1,1}=-a_{1,2} and Y the set of 2x2 matrices with a_{1,1}=-a_{2,1}.
(a) Find dim(W) and dim(Y).
(b) Find dim(W intersect Y).
Assignment 3.
279/1(a,d,f),3(a,b),7,9,12,20
Assignment 4.
322/2(b,e),4,5,8,13,17,18,37,42