Find an LU decomposition of the matrix?

Figure 28.2?The operation of LUP-DECOMPOSITION. (a) The input matrix A with the identity permutation of the rows on the left. The first step of the algorithm determines that the element 5 in the black circle in the third row is the pivot for the first column. (b) Rows 1 and 3 are swapped and the permutation is updated. The shaded column and row represent ? and w^T. (c) The vector ? is replaced by ?/5, and the lower right of the matrix is updated with the Schur complement. Lines divide the matrix into three regions: elements of U (above), elements of L (left), and elements of the Schur complement (lower right). (d)?(f) The second step. (g)?(i) The third step. No further changes occur on the fourth (final) step. (j) The LUP decomposition PA = LU.

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0.6 3 2 3 5 4 3 4 -2 3 3 4 -2 2 0.6 1.6 -3.2 5 4 2 2 2 0.6 0.4 -2 0.4 -2 4 -1 -2 3.4 -1 -1 -2 3.4 -1 4 -0.2 -1 4.2 -0.6 (a) (b) (c) 5 4 2 0.4 2 0.4 -0.2 3 5 4 3 5 5 4 2 0.6 1.6 -3.2 0.4-2 0.4 -0.2 0.42 0.4 0.2 0.6 1.6 -3.2 2 0.6 1.6 -3.2 -0.2 -1 4.2 -0.6 4 -0.2 -1 4.2 -0.6 4 -0.2 0.5 4 -0.5 (d) (e) (f) 4 2 0.4 -2 0.4 -0.2 -0.2 0.5 4 -0.5 3 5 4 3 5 5 5 5 4 2 0.4 -2 0.4 -0.2 0.4 -2 0.4 -0.2 -0.2 0.5 4 -0.5 0.4 -3 2 0.6 1.6 -3.2 -0.2 0.5 4 -0.5 0.6 1.6 -3.2 0.6 (g) (h) (i) 2 2 0.6 5 5 4 2 1 0 0 0 0 0 0 1 3 3 4 -2 0.4 0 -2 0.4 -0.2 5 4 -0.2 0.5 4 -0.5 -1 -2 3.4 -1 0.6 0.4 1 -3 (i) 3. 4. 4. 2. 4. 2. 2. 3. 2. 2.