Solve the equations by crammer's rulcx + y + z = 3 ; 2x+z=5, x+2y=-1.
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HSC Commerce 11th
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Sum
Solve the following equations using Cramer’s Rule:
x + 2y – z = 5, 2x – y + z = 1, 3x + 3y = 8
SOLUTION
Given equations are
x + 2y – z = 5
2x – y + z = 1
3x + 3y = 8
i.e. 3x + 3y + 0z = 8
∴ D =
|12-12-11330|
= 1(0 – 3) – 2(0 – 3) – 1(6 + 3)
= – 3 + 6 – 9
= – 6
Dx =
|52-11-11830|
= 5(0 – 3) – 2(0 – 8) + (– 1)(3 + 8)
= – 15 + 16 – 11
= – 10
Dy =
|15-1211380|
= 1(0 – 8) – 5(0 – 3) + 1(6 – 3)
= – 8 + 15 – 13
= – 6
Dz =
|1252-11338|
= 1(– 8 – 3) – 2(16 – 3) + 5(6 + 3)
= – 11 – 26 + 45
= 8
By Cramer’s Rule,
x =
D
D
DxD=-10-6=53
y =
D
D
DyD=-6-6 = 1
z =
D
D
DzD=8-6=-43
∴ x =
and
53,y=1andz=-43 are the solution of the given equations.
Concept: Application of Determinants - Cramer’s Rule
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Chapter 6: Determinants - Exercise 6.3