.____ _.__ _._.._ ._. J__. ____. 9. [2+2+2pt] Let us use the LUdecomposition to compute the inverse of a matrixa. (a) Describe an algorithm that uses the LEI-decomposition of an n x 71. matrix A for computing A'1 by solving n systems of equations (one for each unit vector). (b) Calculate the floating point operation count of this algorithm. (c) Improve the algorithm by taking advantage of the structure (i.e., the zero entries see question 5a) of the right-hand side. What is the new algorithm's floating point operation count