Solve the following system of linear equations using Cramer's rule : 2x - y + 3z = 9 y - z = -1 x + y - z= 0
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Answer=
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
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