Question

By Gaussion elimination method find the solution of the system: 5x2 + 6x3 = 11 4.C +5X2 + 723 = 16 9x + 2x2 + 3.3 = 15

Answer 1

At first we form a matrix using the coefficients of the given equations

Using that we solve the equations

* 6 یا 315 با 15 2 5 5 2 15 و الله - ما 5 16 6 ۱۹ -3- او - 21 3782 added to oz 5 7 ۱( 5 6 ۱۱ -3 33), 6 واد from third row /33۔ 19/ = > 33 3 = 3 33 Scanned with CamScanner

So we found X_{​​​​​​3} = 13/33 or 0.3939

Substiting this in equation 2

5X₂ + 6(0.3939) = 11

5X₂ + 2.3634 = 11

X_​​​2 = 1.7273

Substiting these values in Equation 1

4X₁ + 5(1.7273) + 7(0.3939) = 16

4X₁ + 11.3938 = 16

4X₁ = 4.6062

X_{​​​​​1} = 1.1515

Note : We can cross check the values by substituting these values into the given equations.