Linear Programming-using simplex method

I have attached an excel file with all the information for the problem and what I used.

Linear Algebra Question

1. Let V be a vector space of odd dimension (greater than 1) over the real field R. Show that any linear operator on V has a proper invariant subspace other than {0}.

Linear Algebra

Let T be a linear operator on a finite dimensional vector space V. Suppose the minimal polynomial for T is of the form P^n where p is an irreducible polynomial over the scalar field. Show that there is a vector x in V such that the T-annihilator of x is p^n.

Linear Algebra

Let A be a 4x4 matrix with minimal polynomial m(t)=(t^2 + 1)(t^2 - 3). Find the rational canonical form for A if A is a matrix over (a) the rational field Q (b)the real field R, (c) the complex field C.

Linear algebra - matricies

Please give step by step instructions and name each step like triangular form, augmented matrix etc so I know when and what to do and can understand it. We are not using calculator so the steps need to be shown to the solution. 1) The augmented matrix of a linear system has been transformed by row operations into the form below. Determine if the system is consistent. 1 5 2 -6 0 4 -7 2 0 0 5 0 2) Is (3,4,-2) a solution of the following system? 5xsub1 - xsub2 +2xsub3 = 7 -2xsub1 + 6xsub2 +9xsub3 = 0 -7xsub1 + 5xsub2 -3xsub3 = -7 3) For what values of h and k is the following system consistent? 2xsub1 - xsub2 = h -6xsub1 +3 xsub2 = k