Linear Algebra Answers

Let K be a division ring with center k. For any a ∈ K\k, show that the ideal generated by x − a in K[x] is the unit ideal.

Let K be a division ring with center k. Show that the center of the polynomial ring R = K[x] is k[x].

Solve by substitution or elimination:
[x+Y=13
[2x-3y=1

a linear algebra question:
let A be an n*n square matrix whose columns form an orthonormal set. Compute A transpose * A

find the inverse to the matrix M =
1 -1 2
-1 3 2
2 1 -3

and use this inverse to solve the system of equations
x-y+2z=1
-x+3y+2z=1
2x+y-3z=5

solve the following system or show that it has no solutions
x+2y=7
-2x+y=1
x-y=-2
3x+y=6

find the inverse to the matrix

M = 2 -3
4 -5

and use this inverse to solve the system of equations
2x-3y=7
4x-5y=15

find the inverse to the matrix

1 -1 2
N= -1 3 2
2 1 -3

and use this inverse to solve the system of equations
x-y+2z=1
-x+3y+2z=1
2x+y-3z=5

The Routh Hurwitz criterion tells us that the eigenvalues of a 2x2 matrix A
with real entries have negative real parts if the determinant of A is positive and the
trace of A (the sum of the entries on the main diagonal) is negative. Prove this.

If x>1 & x>2 means x>2 in real line?