Question

la a² bc 1 2² a
Without expanding the determinant, prove that (1) b b ca = 1 62 63
C c² ab 1 2 2​

Answer 1

Answer:

ANSWER

Consider,

∣

∣

∣

∣

∣

∣

∣

∣

a

b

c

a

2

b

2

c

2

bc

ca

ab

∣

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∣

∣

Multiplying and dividing R

1

by a , R

2

by b and R

3

by c

=

abc

1

∣

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∣

∣

∣

∣

∣

∣

a

2

b

2

c

2

a

3

b

3

c

3

abc

abc

abc

∣

∣

∣

∣

∣

∣

∣

∣

Taking abc common from C

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

∣

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∣

∣

∣

∣

∣

∣

c

1

↔c

3

=−

∣

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∣

∣

∣

∣

1

1

1

a

3

b

3

c

3

a

2

b

2

c

2

∣

∣

∣

∣

∣

∣

∣

∣

(When two rows/columns of a determinant are interchanged, then the value of determinant differs by a negative sign. )

c

2

↔c

3

=

∣

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∣

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∣

∣

∣

∣

1

1

1

a

2

b

2

c

2

a

3

b

3

c

3

∣

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∣

∣