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:

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Inconsistent System of Equations: Definition & Example

from High School Algebra II: Homework Help Resource

Chapter 8 / Lesson 9
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