prove that where a,b,c,d,e are real numbers with (a) not equal to zero. if this linear equation ax+by=c has the same solution set as this one : ax+dy=e, then they are the same equation.

Let V and W be finite dimensional vector spaces over a field F with dimF(V ) = dimF(W ) and let T : V → W be a linear map. Prove there exists an ordered basis A for V and an ordered basis B for W such that [T ]AB is a diagonal matrix where every entry along the diagonal is either a 0 or a 1.

A young couple buying their first home borrow $65,000 for 30 years at 7.4%, compounded monthly, and make payments of $450.05. After 5 years, they are able to make a one-time payment of $2000 along with their 60th payment.

(a) Find the unpaid balance immediately after they pay the extra $2000 and their 60th payment. (Round your answer to the nearest cent.)
$  

(b) How many regular payments of $450.05 will amortize the unpaid balance from part (a)? (Round your answer to the nearest whole number.)
payments

(c) How much will the couple save over the life of the loan by paying the extra $2000? (Use your answer from part (b). Round your answer to the nearest cent.)
$

Let ? be an eigenvalue of a matrix A. Explain why dim(?) ? 1

Problem 3. How many arrangements of MATHEMATICS are there that have ALL of the following properties:

TH appear together in this order and E appears somewhere before C?

Find an equation In slope intercept form passing through the point (-1,4) and parallel to the line 2x+2y=7 Show the steps

Given a right triangle with one leg length of a, one leg length of x-3 and the hypo is x, how does a affect x? Shown on a graph.

I solved for a, it is equal to the square root of 6x-9.... I am having a difficult time interpreting how a affects x.. I am not sure how to graph

Explain the difference between finding the horizontal and vertical asymptotes.

When will there be a point of discontinuity?

What could the graph look like when there is no horizontal or vertical asymptotes.

What is the best trick to be able to draw all polar curves within 5 minutes? Please provide detailed clarification and some examples.

Use f(x) = ?2x, g(x) = square root of x and h(x) = |x| to find and simplify expressions for the following functions and state the domain of each using interval notation. a . (h ? g ? f)(x) b. (h ? f ? g)(x) (g ? f ? h)(x)

Solve the following LP problem using graphical solution method. MAX: 5 X1 + 3 X2 Subject to: 2 X1 − 1 X2 ≤ 2 6 X1 + 6 X2 ≥ 12 1 X1 + 3 X2 ≤ 5 X1, X2 ≥ 0

Discuss understanding how to express quadratic functions to standard forms and graphing polynomial function. This is COLLEGE ALGEBRA.