Mathematics Homework Solutions

3 men paint a fence. How long will it take each of them to paint the fence by himself? Use Gaussian elimination.

Solve using the Gaussian Elimination and show all work. Mike, Joe and Bill are Painting a fence. The painting can be finished if Mike and Joe work together for 4 hours and Bill works alone for 2 hours, or if Mike and Joe work together for 2 hours, and Bill works alone for 5 hours, or if Mike works alone for 6 hours, Joe works ...continues

Complex Cube Roots

Find all the complex cube roots of 2.

Polynomial Proof

Suppose P is a polynomial with real coefficients and P(a+bi)=0. Prove (a-bi)=0

Algebra : Simplify

Simplify y2 /X2 - 4y2 + y/2x + 4y When I have 2 after the y and the x it means squared. These are fractions, in case it is not clear.

Algebra : Solving for X

1/X - X+1/8 = X - 1/4X . These are fractions.

Mathematical Induction : Sum of Square Series

Prove that 1+4+9+...+n^2=n(n+1)(2n+1)/6 by mathematical induction

Let T be a linear map on R^2 defined by T(x,y) = (4x – 2y, 2x + y). Calculate the matrix of T relative to the basis {α1,α2} where α1 = (1,1) , α2 = (-1,0).

Linear Algebra Matrix of the Linear Map Basis of the Linear Space Let T be a linear map on R^2 defined by T(x,y) = (4x – 2y, 2x + y). Calcu ...continues

Linear Algebra: Show that the vectors u1 = (1,2,3), u2 = (0,1,2), u3 = (2,0,1) generate R3(R).

Vector Space and Subspaces Euclidian 3-space Problem:- Show that the vectors u1 = (1,2,3), u2 = (0,1,2), u3 = (2,0,1) generate R3(R). ...continues

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