solving for eigenvalues

A certain 4x4 real matrix is known to have these properties: 1) Two of the eigenvalues of A are L1= 3 and L2= 2. 2) The number 3 is an eigenvalue of the matrix A + 2I. 3) det. A = 12. What are the other 2 eigenvalues of A and what is the characteristic polynomial of A, At, and A-1?

finding eigenvalues

Let Tn = (tij) denote the nxn matrix such that for each index i, tji = a and tij = b for j not = to i. Verify that Tn = (a-b)In + bEn where En is the nxn matrix of all 1's. Find the determinate and the eigenvalues of Tn.

Linear Programming Problem

An office manager needs to buy new filing cabinets. Cabinet A costs $7, and takes up 6 square feet of floor space, and holds 9 cubic feet of files. Cabinet B costs $8, takes up 8 square feet, and holds 13 cubic feet. He has only $66 to spend and the office has room for no more than 60 square feet of cabinets. (Find the Objective Function and the Constraints; Let Cabinet A be "x", and Cabinet B be "y") How many of each can be bought to maximize storage capacity? What is the maximum storage capacity?

linear algebra

Please do NOT send answer back as an attachment. Thank you. To prove a statement "If P then Q", it is valid to prove which of the following statmements instead? A. If not Q then not P B. If Q then P C. If not P then not Q D. Q only if P E. Both P and Q are true

linear algebra

Please do NOT send answer back as an attachment. Thank you. To prove that a statement of the form "If P then Q", you may assume that: A. P=Q B. P is true C. Q is true D. P is false E. nothing until it has been proved