319Matrices and Linear Algebra
Step 5: Row 2 is scaled by remaining nonzero off-diagonal term and subtracted from row 1 to
reduce remaining off-diagonal a
12
term to zero
10
01
15 05
05 02
−
−
The nal matrix in the right is the inverse of the matrix on the left in the rst step. Multiply them to
verify that their product is the identity matrix. We showed this procedure for pedagogical purposes;
we use computers to calculate the inverse of a large matrix.
9.6 SOLVING SYSTEMS OF LINEAR EQUATIONS
Based upon the elements of matrices expressed earlier, you can now apply that information to solv-
ing systems of equations:
41
8
10 30 110
xy
xy
(9.26)
By using the coefcients of the each of the equations as entries in a matrix, we can rewr ...