Homomorphism Problem #1

Please see attached file

Homomorphisms

Please see attached file.

Homomorphisms

Please see attached file.

Homomorphisms

Please see attached file.

Solving Systems of Linear Equations by Graphing

Solve by graphing. I need the step by step solution to this problem, starting off with how does one determine the values of x and y. x-y=3 x+ y = 5

Least square applications

1)We wish to measure a wavefront u(x,y) on a 3X3 grid (see the attached file). The sensor how ever provides us only with differences between grid points. There is sensor noise, so the difference measurements may not be consistent. Number the grid points linearly and set up a set of linear equations (matrix form) relating the ...continues

Difficulty in setting up the constraints for the problem

The famous Y.S. Chang Restaurant is open 24 hours a day. Waiters and busboys report for duty at 3am, 7am, 11am, 3pm, 7pm or 11pm and each works an 8-hour shift. The following table shows the minimum number of workers needed during the six periods into which the day is divided. The scheduling problem is to determine how many w ...continues

Linear Algebra -- Linear Transformations

Please help. I always have a hard time with Linear Algebra. What's the difference between mapping from R3 into R2 and mapping from R2 into R3? Why is the following not a linear transformation from R3 into R2? L(x) = (1 + x1, x2)^T And why is this one not a linear transformation from R2 into R3? L(x) = (x1, x2, 1)^T Th ...continues

Linear Algebra -- Linear Transformations

Let a be a fixed vector in R2. A mapping of the form L(x) = x+a is called a translation. Show that if a does not equal 0, then L is not a linear transformation. Describe or illustrate geometrically the effect of the translation. Thanks for your help!

Linear Algebra -- Linear Transformations

Determine whether the following are linear transformations from C[0,1] into R^1. L(f) = |f(0)| L(f) = [f(0) + f(1)]/2 L(f) = {integral from 0 to 1 of [f(x)]^2 dx}^(1/2) Thanks so much. :)