Question

3. Solve by Cramer’s rule: x + y – z = 3, 2x + 3y + z = 3 , 8y + 3z = 1

Answer 1

Step-by-step explanation:

To solve the system by Cramer's rule, we do the following steps:

1. Write the system as a matrix equation AX=b where:

A=

⎣

⎢

⎢

⎡

3

2

4

1

−4

1

1

3

−3

⎦

⎥

⎥

⎤

X=

⎣

⎢

⎢

⎡

x

y

z

⎦

⎥

⎥

⎤

b=

⎣

⎢

⎢

⎡

2

−1

−11

⎦

⎥

⎥

⎤

2. Next, we find the following determinants:

Δ=

∣

∣

∣

∣

∣

∣

∣

∣

3

2

4

1

−4

1

1

3

−3

∣

∣

∣

∣

∣

∣

∣

∣

=∣A∣=63

Δ

1

=

∣

∣

∣

∣

∣

∣

∣

∣

2

−1

−11

1

−4

1

1

3

−3

∣

∣

∣

∣

∣

∣

∣

∣

=−63

Δ

2

=

∣

∣

∣

∣

∣

∣

∣

∣

3

2

4

2

−1

−11

1

3

−3

∣

∣

∣

∣

∣

∣

∣

∣

=126

Δ

3

=

∣

∣

∣

∣

∣

∣

∣

∣

3

2

4

1

−4

1

2

−1

−11

∣

∣

∣

∣

∣

∣

∣

∣

=189

3. The solution is now given by:

x=

Δ

Δ

1

=−1

y=

Δ

Δ

2

=2

z=

Δ

Δ

3

=3