Linear Algebra Answers

If A is an 7 x 7 matrix with all 49 entries being odd numbers. Show that det (A) is a multiple of 64. You may use the fact (without proving) that an n x n matrix with integer entries has an integer determinant.

If X and Y are n*n matrices, Show that (I-XY) is invertible if and only if (I-YX) is
invertible.
Hint: Use X(I-YX)=(I-XY)X

Assess what the results of the regression equation tells managers and how it is likely to impact decisions made related to maximizing profitability.

matrix[2x_5y]+matrix[x-y_-6x]=matrix[6_2]

solve the following equation for x and y.

Let K be a division ring with center k. Show that any ideal I ⊆ R has the form R • h where h ∈ k[x].

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