# x + 2y = 6 2x + 4y = 13 (a) Write this system of equations in matrix form (b) What happens when...

## Question:

{eq}\left\{\begin{matrix} x + 2y = 6 \\ 2x + 4y = 13 \end{matrix}\right. {/eq}

(a) Write this system of equations in matrix form

(b) What happens when you try to solve by multiplying by {eq}A^{-1} {/eq}?

## System of Equations:

The given system of equations in a matrix form is a of order {eq}2\times 2 {/eq} . To find the solution of the system of equations first we find the system in matrix form. If the determinant of the matrix is zero then system has no solution.

## Answer and Explanation:

Consider the system of equations

{eq}\displaystyle x+2y=6\\ \displaystyle 2x+4y=13 {/eq}

Rewrite the system of equations in matrix form {eq}\displaystyle \, \, AX=b {/eq}

{eq}\displaystyle \begin{bmatrix} 1 &2 \\ 2&4 \end{bmatrix} \begin{bmatrix} x\\y \end{bmatrix}=\begin{bmatrix} 6\\13 \end{bmatrix} {/eq}

(b)

{eq}\displaystyle \left |A \right |= \begin{vmatrix} 1 &2 \\ 2&4 \end{vmatrix} =4-4=0 {/eq}

The determinant of the matrix is zero. Therefore, the matrix is singular and it has no solution.

#### Learn more about this topic:

Inconsistent System of Equations: Definition & Example

from High School Algebra II: Homework Help Resource

Chapter 8 / Lesson 9
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