Cramer's Rule Pdf - Buaft.com

Cramer’s rule PDF

consider the following system of equation.

a.x + b y = m………………..1

c x +d y =n…………………….2

We know that

AX = B

Where

$cramer,s rule pdf proof$

Ax =B can be written as

$cramer's rule pdf$

also, this form can be written as

$\large X= \frac{AdjA}{|A|}\, \times \, \, B$

Also, can be written as in the form

$cramer'rule pdf proof$

$cramer's rule pdf$

$cramer rule pdf proof where x equal to$

$cramer's rule pdf proof where y equal to$

this complete the proof of crammer’s rule

Cramer’s rule PDF:

Example:

we solve the following system by using matrix inversion method

4x-2y=8

3x+y=-4

SOLUTION:

STEP: 1

$cramer's rule pdf$

STEP: 2

the coefficient of matrix $cramer's rule pdf$

det M= 4×1-3(-2)= 4+6=10 ≠ 0

$\large M^{-1}$ is possible

STEP : 3

$cramer's rule pdf$

$\large =\frac{1}{10}\begin{bmatrix} 8-8\\ -24-26 \end{bmatrix}$

$\large =\frac{1}{10}\begin{bmatrix} 0\\ -40 \end{bmatrix}=\begin{bmatrix} 0\\ -4 \end{bmatrix}$

hence

$\large \begin{bmatrix} x\\ y \end{bmatrix}=\begin{bmatrix} 0\\ -4 \end{bmatrix}$

there is

x=0 and y = -4

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