Login/Sign Up
Home » Solve each of the following systems of equations using matrix method. ; ; .
Solve each of the following systems of equations using matrix method.
x - 2y + z = 0;
y - z = 2;
2x - 3z = 10.
CBSE | Class 12 | Excercise 8A | Maths | RS Aggarwal | System of Linear Equations
Solve each of the following systems of equations using matrix method.
x - 2y + z = 0;
y - z = 2;
2x - 3z = 10.

Solution:

We need to find: -\mathrm{x}, \mathrm{y}, \mathrm{z}
The given set of lines are : –
\begin{array}{l} x-2 y+z=0 \\ y-z=2 \\ 2 x-3 z=10 \end{array}
Now converting the following equations in matrix form,
\begin{array}{l} \mathrm{AX}=\mathrm{B} \\ {\left[\begin{array}{ccc} 1 & -2 & 1 \\ 0 & 1 & -1 \\ 2 & 0 & -3 \end{array}\right]\left[\begin{array}{l} x \\ y \\ z \end{array}\right]=\left[\begin{array}{c} 0 \\ 2 \\ 10 \end{array}\right]} \\ \mathrm{R}_{3}-2 \mathrm{R}_{1} \\ {\left[\begin{array}{ccc} 1 & -2 & 1 \\ 0 & 1 & -1 \\ 0 & 4 & -5 \end{array}\right]\left[\begin{array}{l} x \\ y \\ z \end{array}\right]=\left[\begin{array}{c} 0 \\ 2 \\ 10 \end{array}\right]} \\ \mathrm{R}_{3}-4 \mathrm{R}_{2} \\ {\left[\begin{array}{ccc} 1 & -2 & 1 \\ 0 & 1 & -1 \\ 0 & 0 & -1 \end{array}\right]\left[\begin{array}{l} x \\ y \\ z \end{array}\right]=\left[\begin{array}{l} 0 \\ 2 \\ 2 \end{array}\right]} \end{array}
Again on converting back into equations we get
\begin{array}{l} X-2 y+z=0 \\ Y-z=2 \\ -z=2 \\ Z=-2 \\ Y+2=2 \\ Y=0 \\ X+0-2=0 \\ X=2 \\ \therefore x=2, y=0, z=-2 \end{array}

i

More Material