Question

X+y+z=2,x+2y+3z=1,3X+Y-5Z=4 solve the following equations by cramers rule

Answer 1

Answer:

Solution

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Correct option is A)

Given equations are,

x+y+z=2

x+2y+z=1

3x+y−5z=4

Coefficient matrix =

⎣

⎢

⎢

⎡

1

1

3

1

2

1

1

1

−5

⎦

⎥

⎥

⎤

△=

∣

∣

∣

∣

∣

∣

∣

∣

1

1

3

1

2

1

1

1

−5

∣

∣

∣

∣

∣

∣

∣

∣

=1(−10−1)−1(−5−3)+1(1−6)=−11+8−5=−8

△

1

=

∣

∣

∣

∣

∣

∣

∣

∣

2

1

4

1

2

1

1

1

−5

∣

∣

∣

∣

∣

∣

∣

∣

=2(−10−1)−1(−5−4)+1(1−8)=−22+9−7=−20

△

2

=

∣

∣

∣

∣

∣

∣

∣

∣

1

1

3

2

1

4

1

1

−5

∣

∣

∣

∣

∣

∣

∣

∣

=1(−5−4)−2(−5−3)+1(4−3)=−9+16+1=8

△

3

=

∣

∣

∣

∣

∣

∣

∣

∣

1

1

3

1

2

1

2

1

4

∣

∣

∣

∣

∣

∣

∣

∣

=1(8−1)−1(4−3)+2(1−6)=7−1−10=−4

x=

△

△

1

=

−8

−20

=

2

5

y=

△

△

2

=

−8

8

=−1

z=

△

△

3

=

−8

−4

=

2

1

∴x=

2

5

,y=−1 and z=

2

1

Hence solved.