Question

4) a) For the system of equations given, partially row reduce the coefficient matrix in the following careful way: *1 + 2y, - 2 = 5 4x1 +9y1 - 32 = 8 (5x + 12y - 321 = 1 Stage 1: just reduce the matrix first to an upper triangular form U and leave pivot entries as they are (don't multiple to change them to 1's). Reduce from left to right through the columns and from the pivot entry down within a given column. To accomplish this, you will only have to use the row operation that adds a multiple of one row to another row, not the other two. Write down the matrix corresponding to each such row operation. So for example, if I add -2* row 1 to row 3, that would 0 01 correspond to multiplying on the left by the matrix 0. Keep track of these matrices that are 0 used, and of the order in which they are used, so for each row operation, you are multiplying the matrix on the left by another elementary matrix of this form. When you are done, you will have LA = U, where L is the product of the elementary matrices in the right order. 1 1 Stage 2: left-multiply both sides of the equation by the inverse of Ly, to obtain A = LU where L = 271 b) Use the matrix Lr to compute what the augmented column would be changed to in part (a). c) Put (a) and (b) together to write the solution set in the form x = x + in where åp is a particular solution to the system, and in is the solution to the associated homogeneous system.

Answer 1