Chapter 9.6, Problem 10P

(a)

To determine

To show: That $a_{11}+a_{22}<0$ and $a_{11}{a}_{22}-a_{12}{a}_{21}>0$ of the linear system by using the given data.

(b)

To determine

To show: The results $A=-\frac{a_{21}^2+a_{22}^2+\left(a_{11}{a}_{22}-a_{12}{a}_{21}\right)}{2\Delta },B=\frac{a_{12}{a}_{22}+a_{11}{a}_{21}}{\Delta },C=-\frac{a_{11}^2+a_{12}^2+\left(a_{11}{a}_{22}-a_{12}{a}_{21}\right)}{2\Delta }$ by using the given data.

(c)

To determine

To show: That $A>0$ and $4AC-B^2=\frac{\left(a_{11}^2+a_{12}^2+a_{21}^2+a_{22}^2\right)\left(a_{11}{a}_{22}-a_{12}{a}_{21}\right)+2{\left(a_{11}{a}_{22}-a_{12}{a}_{21}\right)}^2}{{\Delta }^2}>0$ by using the result of part (a).