Chapter 16.1, Problem 1WE

To determine

To find: the value of given variable.

Answer to Problem 1WE

  $x=\frac{1}{a-b},y=-\frac{b}{a-b}$ .

Explanation of Solution

Given information:

Given symbol,

  $\left[\begin{array}{c}ax+y\\ bx+y\end{array}\right]=\left[\begin{array}{c}1\\ 0\end{array}\right]$

Calculation: Now, $\left[\begin{array}{c}ax+y\\ bx+y\end{array}\right]=\left[\begin{array}{c}1\\ 0\end{array}\right]$

Since the matrices are equal elements in corresponding positions are equal.

Therefore, $ax+y=1$ and $bx+y=0$

  $\begin{array}{l}\underset{\_}{\begin{array}{l}ax+y=1\\ bx+y=0\end{array}}\\ ax-bx=1\\ x=\frac{1}{a-b}\end{array}$

Now,

  $\begin{array}{c}bx+y=0\\ b\cdot \frac{1}{a-b}+y=0\\ y=-\frac{b}{a-b}\end{array}$

Therefore, $x=\frac{1}{a-b},y=-\frac{b}{a-b}$ .