## 1.3 Exercises on solving systems of linear equations: matrix inversion and Cramer's rule

- Use Cramer's rule to find the values of
*x*and*y*that solve the following two equations simultaneously.3 *x*−2 *y*= 11 2 *x*+*y*= 12 We have*x*=11 −2 12 1 / 3 −2 2 1 = 5 *y*=3 11 2 12 / 3 −2 2 1 = 2. - Solve the two equations in the previous problem by using matrix inversion.
Solution is
(1/7) 1 2 −2 3 11 12 = 5 2 - Use Cramer's rule to find the values of
*x*,*y*, and*z*that solve the following three equations simultaneously.4 *x*+3 *y*−2 *z*= 7 *x*+*y*= 5 3 *x*+*z*= 4 We have*x*=7 3 −2 5 1 0 4 0 1 / 4 3 −2 1 1 0 3 0 1 = 0 *y*=4 7 −2 1 5 0 3 4 1 / 4 3 −2 1 1 0 3 0 1 = 5 *z*=4 3 7 1 1 5 3 0 4 / 4 3 −2 1 1 0 3 0 1 = 4 - Solve the three equations in the previous problem by using matrix inversion.
Solution is
(1/7) 1 −3 2 −1 10 −2 −3 9 1 7 5 4 = 0 5 4