Chapter 6.2, Problem 30E

Consider two distinct real numbers, a and b. We definethe function
$f\left(t\right)=\det \left[\begin{array}{ccc}1& 1& 1\\ a& b& t\\ a^2& b^2& t^2\end{array}\right]$
a. Show that $f\left(t\right)$ is a quadratic function. What is thecoefficient of $t^2$ ?
b. Explain why $f\left(a\right)=f\left(b\right)=0$ . Conclude that $f\left(t\right)=k\left(t-a\right)\left(t-b\right)$ , for some constant k. Find k,using your work in part (a).
c. For which values of t is the matrix invertible?