Consider the system of equations 2 x + 4 y = 1 2 x + 2 y = 3. (a) How can you write this system...


Consider the system of equations

{eq}2 x + 4 y = 1\\ 2 x + 2 y = 3 {/eq}.

(a) How can you write this system in matrix form {eq}Ax = b {/eq}?

(b) What is the inverse of the matrix {eq}A {/eq}?

(c) Solve the linear system for {eq}\begin{bmatrix} x\\ y \end{bmatrix} {/eq} by multiplying both sides on the left by {eq}A^{-1} {/eq}.

Solving linear equations using matrix

To find the solution of linear equation first represent it in form {eq}AX=B \\ X=A^{-1}B {/eq}

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{eq}2 x + 4 y = 1 \\ 2 x + 2 y = 3 \\ {/eq}

(a) Above equation can be represent as

{eq}A= \begin{bmatrix} 2 & 4 \\ 2 & 2 \end{bmatrix}...

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System of Linear Equations: Definition & Examples


Chapter 8 / Lesson 8

Learn the linear equation definition, understand the meaning of linear equations, see systems of linear equations, and learn how to solve a system of linear equations through linear equation examples. Practice writing systems of linear equations and finding a solution to a system of linear equations.

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