The inverse of a matrix can also be computed by solving several systems of equations using the method of Example 3.34. For an n X n matrix A, to find its inverse we need to solve AX = In for the n × n matrix X. Writing this equation as A [x1 x2 · · xn] = [ e1 e2 · · · en] , using the matrix-column form of AX, we see that we need to solve n systems of linear equations: Ax1 = e1, Ax2 = e2, . . . , AXn = en· Moreover, we can use the factorization A = LU to solve each one of these systems.
In Exercises, use the approach just outlined to find A - l for the given matrix. Compare with the method of Exercises.
a. A in Exercise 1

b. A in Exercise 4

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