Question

[xa ya zc] [x y z]
[a² b² c²]=[a b c]
[1 1 1] [bc ca ab]
[xa ya zc] [x y z]
[a² b² c²]=[a b c]
[1 1 1] [bc ca ab]
without expanding determine show that LHS=RHS​​

Answer 1

Answer:

LHS :

∣

∣

∣

∣

∣

∣

∣

∣

a

b

c

a

2

b

2

c

2

bc

ca

ab

∣

∣

∣

∣

∣

∣

∣

∣

=

abc

1

∣

∣

∣

∣

∣

∣

∣

∣

a

2

b

2

c

2

a

3

b

3

c

3

abc

abc

abc

∣

∣

∣

∣

∣

∣

∣

∣

[R

1

→aR

1

,R

2

→bR

2

,R

3

→cR

3

]

=

abc

abc

∣

∣

∣

∣

∣

∣

∣

∣

a

2

b

2

c

2

a

3

b

3

c

3

1

1

1

∣

∣

∣

∣

∣

∣

∣

∣

=

∣

∣

∣

∣

∣

∣

∣

∣

a

2

b

2

c

2

a

3

b

3

c

3

1

1

1

∣

∣

∣

∣

∣

∣

∣

∣

=

∣

∣

∣

∣

∣

∣

∣

∣

1

1

1

a

2

b

2

c

2

a

3

b

3

c

3

∣

∣

∣

∣

∣

∣

∣

∣

=RHS [C

1

↔C

3

,C

2

↔C

3

]