Q. 145.0( 3 Votes )

Solve the followi

Answer :

Given: - Equations are: –


x + y = 5


y + z = 3


x + z = 4


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


x + y = 5


y + z = 3


x + z = 4


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



Solving determinant, expanding along 1st Row


D = 1[1] – 1[ – 1] + 0[ – 1]


D = 1 + 1 + 0


D = 2


D = 2


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


Here




Solving determinant, expanding along 1st Row


D1 = 5[1] – 1[(3)(1) – (4)(1)] + 0[0 – (4)(1)]


D1 = 5 – 1[3 – 4] + 0[– 4]


D1 = 5 – 1[ – 1] + 0


D1 = 5 + 1 + 0


D1 = 6


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


Here




Solving determinant


D2 = 1[3 – 4] – 5[ – 1] + 0[0 – 3]


D2 = 1[ – 1] + 5 + 0


D2 = 4


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


Here




Solving determinant, expanding along 1st Row


D3 = 1[4 – 0] – 1[0 – 3] + 5[0 – 1]


D3 = 1[4] – 1( – 3) + 5( – 1)


D3 = 4 + 3 – 5


D3 = 2


Thus by Cramer’s Rule, we have




x = 3


again,




y = 2


and,




z = 1


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