Chapter 12.4, Problem 13PPSE

Solution

To find: To write the system as a matrix equation. To identify the coefficient matrix, the variable matrix and the constant matrix.

The matrix equation is $\left[\begin{array}{cc}3& 5\\ 1& 1\end{array}\right]\left[\begin{array}{c}a\\ b\end{array}\right]=\left[\begin{array}{c}0\\ 2\end{array}\right]$ .

Given information:

Given,system is:

  $\begin{array}{c}3a+5b=0\\ a+b=2\end{array}$

Calculation:

Writing the coefficients as the elements of a matrix to obtain the coefficient matrixA :

  $\left[\begin{array}{cc}3& 5\\ 1& 1\end{array}\right]$

The variables of the equation are written as the variable matrix X :

  $\left[\begin{array}{c}a\\ b\end{array}\right]$

Writing the constants as the elements of a matrix to obtain the constant matrix B :

  $\left[\begin{array}{c}0\\ 2\end{array}\right]$ .

Hencethe matrix equation is given by:

  $\left[\begin{array}{cc}3& 5\\ 1& 1\end{array}\right]\left[\begin{array}{c}a\\ b\end{array}\right]=\left[\begin{array}{c}0\\ 2\end{array}\right]$ .

Conclusion:

The matrix equation is $\left[\begin{array}{cc}3& 5\\ 1& 1\end{array}\right]\left[\begin{array}{c}a\\ b\end{array}\right]=\left[\begin{array}{c}0\\ 2\end{array}\right]$ .