Chapter 7, Problem 12PS

(A)

To determine

To find:

The value of constants should be given to $a,b,c$

Answer to Problem 12PS

The form of matrix $A=\left[\begin{array}{c}-1\\ 2\\ 3\end{array}\right]$

Explanation of Solution

Given:

The system of linear equation

  $\begin{array}{l}x+2y-3z=a\\ -x-y+z=b\\ 2x+3y-2z=c\end{array}$

Concept used:

The Matrix equation

  $AX=B$

Where A is the coefficient matrix of the system

  $X$ And $B$ are column matrices

The column matrix $B$ is also called a constant matrix its entries are the constant terms in the system of equation

Calculation:

The system of linear equation

  $\begin{array}{l}x+2y-3z=a\\ -x-y+z=b\\ 2x+3y-2z=c\end{array}$

The Matrix equation

  $AX=B\mathrm{.................}\left(1\right)$

Where A is the coefficient matrix of the system

  $X$ And $B$ are column matrices

  $A=\left[\begin{array}{ccc}1& 2& -3\\ -1& -1& 1\\ 2& 3& -2\end{array}\right],X=\left[\begin{array}{c}x\\ y\\ z\end{array}\right],B=\left[\begin{array}{c}a\\ b\\ c\end{array}\right]$

From equation (1)

  $\left[\begin{array}{ccc}1& 2& -3\\ -1& -1& 1\\ 2& 3& -2\end{array}\right]\left[\begin{array}{c}x\\ y\\ z\end{array}\right]=\left[\begin{array}{c}a\\ b\\ c\end{array}\right]$

The matrix by using on augmented matrix $\left[A:B\right]$

An elementary row operations are applied to a matrix to obtain a (row-equivalent) row echelon form of the matrix.

The augmented matrix