Question

solve the following equationsby using cramers rule 1x-2y+3z=0,2x+1y-3z=5,-1x-1y+2z=3​

Answer 1

Step-by-step explanation:

Question

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Solve the following equations using Cramer's Rule

2x−y+3z=9,x+y+z=6,x−y+z=2

Medium

Solution

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Δ=

∣

∣

∣

∣

∣

∣

∣

∣

2

1

1

−1

1

−1

3

1

1

∣

∣

∣

∣

∣

∣

∣

∣

=2(1+1)−(−1)(1−1)+3(−2)=4−6=−2

Now, Δ

x

=

∣

∣

∣

∣

∣

∣

∣

∣

9

6

2

−1

1

−1

3

1

1

∣

∣

∣

∣

∣

∣

∣

∣

=14

Δ

y

=

∣

∣

∣

∣

∣

∣

∣

∣

2

1

1

9

6

2

3

1

1

∣

∣

∣

∣

∣

∣

∣

∣

=−2

Δ

z

=

∣

∣

∣

∣

∣

∣

∣

∣

2

1

1

−1

1

−1

9

6

2

∣

∣

∣

∣

∣

∣

∣

∣

=−6

So,According to Cramer's Rule x=

Δ

Δ

x

=

−2

14

=−7

y=

Δ

Δ

y

=

−2

−2

=1

z=

Δ

Δ

z

=

−2

−6

=3