4. Let V and W be vector spaces. Suppose {v1, ..., Un} is a basis of V and {w1,..., wm} is a basis for W. Prove that the linear map L :V → W defined by L(v;) (Hence, if vector spaces V and W have the same dimension, then they are isomorphic.) = w; (for all i E {1,.., n}) is an isomorphism.

A tortoise and hare are competing in a 400-meter race. The arrogant hare gives the tortoise a 220-meter head start. When the start gun is fired, the hare begins running at a constant speed of 3.5 meters per second and the tortoise begins crawling at constant speed of 1.5 meters per second. Take out a piece of paper and read the above problem context again. You will prepare your written work and solutions on your own paper and upload it and the end of this question. Complete the problem solving process by: i. reading and re-reading the problem to identify the quantities in the situation; ii. making a drawing to represent the relevant quantities in the situation; iii. and defining the variable t to represent the number of seconds since the start of the race. a. Define a function f to determine the distance of the tortoise from the finish line in terms of the number of seconds, t, since the start of the race. Preview Solve f(t) = 0 and describe what your solution represents. t = Preview…

Solve AT(CBT).

Can you also solve part D? Using this follow-up question for an additional subpart

True or false: There are integer solutions to the linear Diophantine equation 903x + 731y =1106. Justify your answer