Chapter 12.4, Problem 62PPSE

Solution

To find: To explain how to the matrix equation that represents the system.

The matrix equation is $\left[\begin{array}{ccc}2& -3& 1\\ 1& 4& -2\\ 3& 2& -3\end{array}\right]\left[\begin{array}{c}x\\ y\\ z\end{array}\right]=\left[\begin{array}{c}-10\\ 11\\ 7\end{array}\right]$

Given information:

Given,system is:

  $\begin{array}{c}2x-3y+z+10=0\\ x+4y=2z+11\\ -2y+3z+7=3x\end{array}$

Calculation:

Rewriting the equations with variables on one side and constants on other side:

  $\begin{array}{c}2x-3y+z=-10\\ x+4y-2z=11\\ 3x+2y-3z=7\end{array}$

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

  $\left[\begin{array}{ccc}2& -3& 1\\ 1& 4& -2\\ 3& 2& -3\end{array}\right]$

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

  $\left[\begin{array}{c}x\\ y\\ z\end{array}\right]$

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

  $\left[\begin{array}{c}-10\\ 11\\ 7\end{array}\right]$ .

Hencethe matrix equation is given by:

  $\left[\begin{array}{ccc}2& -3& 1\\ 1& 4& -2\\ 3& 2& -3\end{array}\right]\left[\begin{array}{c}x\\ y\\ z\end{array}\right]=\left[\begin{array}{c}-10\\ 11\\ 7\end{array}\right]$

Conclusion:

The matrix equation is $\left[\begin{array}{ccc}2& -3& 1\\ 1& 4& -2\\ 3& 2& -3\end{array}\right]\left[\begin{array}{c}x\\ y\\ z\end{array}\right]=\left[\begin{array}{c}-10\\ 11\\ 7\end{array}\right]$