(Application: Operation Counts & Time Complexity) A computer stores numbers as "floating points." Computers can add and multiply two such floating points. Gaussian elimination of an n X n matrix (for n large) requires roughly n3 such floating point opera- tions. A standard 2.5 GHz processor can perform roughly 1010 FLoating point Operations Per Second, or 10 GFLOPS For each of the following, explain/show your work and, in complete sentences, comment on how the answer you found compares with your expectations. (a) Approximately how long will it take a standard computer to use Gaussian elimination to solve a matrix equation where A is a 1000 x 1000 matrix? (Compare this with how long you think it would take you.) (b) We have previously shown that a 4K display has about 8 million pixels, and each pixel has 3 numbers to describe reds, greens, and blues. A filter on this image can be understood as an 24 million by 24 million matrix. Approximately how long would it take for a standard computer to use Gaussian elimination to put the this matrix into reduced row echelon form? (c) Explain why it is so important to be efficient with our computations