Question

2. Solve into Matrix method:
2 x - y + 3 z = 9
X+y+ z = 6
x-y+z= 2​

Answer 1

Answer:

Solve the following system of equations by using Matrix inversion method.

2x−y+3z=9,x+y+z=6,x−y+z=2

Answer

Given

2x−y+3z=9 ………..(1)

x+y+z=6 …………..(2)

x−y+z=2 …………….(3)

using matrix inversion method

AX=B

⎣

⎢

⎢

⎡

2

1

1

−1

1

−1

3

1

1

⎦

⎥

⎥

⎤

⎣

⎢

⎢

⎡

x

y

z

⎦

⎥

⎥

⎤

=

⎣

⎢

⎢

⎡

9

6

2

⎦

⎥

⎥

⎤

and X=A

−1

B where A

−1

=

∣A∣

adj(A)

Now adjA=

⎣

⎢

⎢

⎡

2

0

−2

−2

−1

−1

−4

1

3

⎦

⎥

⎥

⎤

∣A∣=2(1+1)−1(1−1)+3(−1−1)

∣A∣=4−6

∣A∣=−2.

Now A

−1

=

2

−1

⎣

⎢

⎢

⎡

2

0

−2

−2

−1

−1

−4

1

3

⎦

⎥

⎥

⎤

Now X=A

−1

B

⎣

⎢

⎢

⎡

x

y

z

⎦

⎥

⎥

⎤

=

2

−1

⎣

⎢

⎢

⎡

2

0

−2

−2

−1

−1

−4

1

3

⎦

⎥

⎥

⎤

⎣

⎢

⎢

⎡

9

6

2

⎦

⎥

⎥

⎤

⎣

⎢

⎢

⎡

x

y

z

⎦

⎥

⎥

⎤

=

2

−1

⎣

⎢

⎢

⎡

18−12−8

0−6+2

−18−6+6

⎦

⎥

⎥

⎤

=

2

−1

⎣

⎢

⎢

⎡

−2

−4

−18

⎦

⎥

⎥

⎤

⎣

⎢

⎢

⎡

x

y

z

⎦

⎥

⎥

⎤

=

⎣

⎢

⎢

⎡

1

2

9

⎦

⎥

⎥

⎤

Hence [x=1,y=2 & z=9].

Answer 2

$\huge \mathfrak \red{ U R \:ans \: gd \: morning}$