Answer :

Given: - Equations are: –


6x + y – 3z = 5


X + 3y – 2z = 5


2x + y + 4z = 8


Tip: - Theorem – Cramer’s Rule


Let there be a system of n simultaneous linear equations and with n unknown given by







and let Dj be the determinant obtained from D after replacing the jth column by



Then,


provided that D ≠ 0


Now, here we have


6x + y – 3z = 5


x + 3y – 2z = 5


2x + y + 4z = 8


So by comparing with theorem, lets find D , D1 and D2



Solving determinant, expanding along 1st Row


D = 6[(4)(3) – (1)( – 2)] – 1[(4)(1) + 4] – 3[1 – 3(2)]


D = 6[12 + 2] – [8] – 3[ – 5]


D = 84 – 8 + 15


D = 91


Again, Solve D1 formed by replacing 1st column by B matrices


Here




Solving determinant, expanding along 1st Row


D1 = 5[(4)(3) – ( – 2)(1)] – 1[(5)(4) – ( – 2)(8)] – 3[(5) – (3)(8)]


D1 = 5[12 + 2] – 1[20 + 16] – 3[5 – 24]


D1 = 5[14] – 36 – 3( – 19)


D1 = 70 – 36 + 57


D1 = 91


Again, Solve D2 formed by replacing 1st column by B matrices


Here




Solving determinant


D2 = 6[20 + 16] – 5[4 – 2( – 2)] + ( – 3)[8 – 10]


D2 = 6[36] – 5(8) + ( – 3)( – 2)


D2 = 182


And, Solve D3 formed by replacing 1st column by B matrices


Here




Solving determinant, expanding along 1st Row


D3 = 6[24 – 5] – 1[8 – 10] + 5[1 – 6]


D3 = 6[19] – 1( – 2) + 5( – 5)


D3 = 114 + 2 – 25


D3 = 91


Thus by Cramer’s Rule, we have




x = 1


again,




y = 2


and,




z = 1


Rate this question :

How useful is this solution?
We strive to provide quality solutions. Please rate us to serve you better.
Try our Mini CourseMaster Important Topics in 7 DaysLearn from IITians, NITians, Doctors & Academic Experts
Dedicated counsellor for each student
24X7 Doubt Resolution
Daily Report Card
Detailed Performance Evaluation
caricature
view all courses
RELATED QUESTIONS :

Three schools A, Mathematics - Board Papers

Using properties Mathematics - Board Papers

Two schools A andMathematics - Board Papers

State True or FalMathematics - Exemplar