This is a Linear Algebra Problem

Prove that a module over a polynomial ring C[t] is a finite dimensional vector space with a linear operator that plays the role of multiplication by t.

Linear Algebra

Give an example of a ring which is not a principle ideal domain.

solve and answer COMPLETE...please do not post with out complete answers

several state and federal government spokespersons who use linear equations in a variety of ways. 1. An employee of the National Parks Service told you about a location in Washington, DC. It is a large grassy area south of the White House known as the Ellipse. The National Tree Lighting Ceremony is held annually on the Ellipse. Because the President officiates at this event, the Secret Service makes calculations which they use in planning security. The Ellipse is actually an ellipse with major axis of length 1048 ft. and minor axis of length 898 ft. Assuming that a coordinate system is superimposed on the area in such a way that the center is at the origin and the major and minor axes are... click for more

symplectic matrices

Interesting properties of a symplectic matrix. See attached for details.

Review

(See attached file for full problem description) --- 1. Solve the following system of simultaneous equations: 6x1 + 4x2 = 40 2x1 + 3x2 = 20 x1 = ??? put your answer in the form x or x.x 2. Max Z = 5x1 + 3x2 Subject to: 6x1 + 2x2 <= 18 15x1 + 20x2 <= 60 x1 , x2 >= 0 Find the optimal profit. Z=? put your answer in the form x.xxx 3. Consider the following linear programming problem. MIN Z = 10x1 + 20x2 Subject to: x1 + x2 >= 12 2x1 + 5x2 >= 40 x2 >= 13 x1, x2 >= 0 What is minimum cost Z=?? Put your answer in the x.xxx (to three decimal places) --- (See attached file for full problem description)