Name: Solving System of Linear Equations using Matrices
Uploaded: 2019-07-19
Duration: 11 min 30 s
Description: A system of linear equations can be represented in matrix form using its coefficient, variable and constant matrices. Learn about the inverse matrix method!

Question

Solve each of the following systems of equations using matrix method.

$3 x - 4 y + 2 z = - 1$ ,

$2 x + 3 y + 5 z = 7$ ,

x + z = 2

Accepted Answer

We have to find: $3 x - 4 y + 2 z = - 1$

Given set of lines are:

$3 x - 4 y + 2 z = - 1$ ,

$2 x + 3 y + 5 z = 7$ ,

$x + z = 2$

Converting the following equations in matrix form,

$A X = B$

$[\begin{matrix} 3 & - 4 & 2 \\ 2 & 3 & 5 \\ 1 & 0 & 1 \end{matrix}] [\begin{matrix} x \\ y \\ z \end{matrix}] = [\begin{matrix} - 1 \\ 7 \\ 2 \end{matrix}]$

Applying row operations: $R_{2} \to 3 R_{2} - 2 R_{1}$ and $R_{3} \to 3 R_{3} - R_{1}$

$[\begin{matrix} 3 & - 4 & 2 \\ 0 & 17 & 11 \\ 0 & 4 & 1 \end{matrix}] [\begin{matrix} x \\ y \\ z \end{matrix}] = [\begin{matrix} - 1 \\ 23 \\ 7 \end{matrix}]$

Applying row operation: $R_{3} \to 11 R_{3} - R_{2}$

$[\begin{matrix} 3 & - 4 & 2 \\ 0 & 17 & 11 \\ 0 & 27 & 0 \end{matrix}] [\begin{matrix} x \\ y \\ z \end{matrix}] = [\begin{matrix} - 1 \\ 23 \\ 54 \end{matrix}]$

Again converting into equations, we get

$3 x - 4 y + 2 z = - 1$

$17 y + 11 z = 23$

$27 y = 54$ $\Rightarrow y = 2$

Putting the value of $y$ in $17 y + 11 z = 23$

$17 \times 2 + 11 z = 23$

$11 z = 23 - 34$ $\Rightarrow z = - 1$

Putting values in $3 x - 4 y + 2 z = - 1$

$3 x - 4 \times 2 + 2 \times - 1 = - 1$

$3 x = - 1 + 8 + 2$

$3 x = 9$ $\Rightarrow x = 3$

$∴$ $x = 3, y = 2, z = - 1$

Solve each of the following systems of equations using matrix method.

$3 x - 4 y + 2 z = - 1$ ,

$2 x + 3 y + 5 z = 7$ ,
$x + z = 2$

Important Questions on System of Linear Equations

Learn and Prepare for any exam you want !

Solve each of the following systems of equations using matrix method. 3x-4y+2z=-1, 2x+3y+5z=7, x+z=2

Important Questions on System of Linear Equations

Learn and Prepare for any exam you want !

Solve each of the following systems of equations using matrix method.

$3 x - 4 y + 2 z = - 1$ ,

$2 x + 3 y + 5 z = 7$ ,
$x + z = 2$