Question

2. x-y = 3,
* + Ž = 6.
$\frac{1}{2} (x + 3) - \frac{2}{5} (x - 3 = x + 9$
​

Answer 1

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Class 12

>>Maths

>>Determinants

>>Introduction to Determinants

>>prove that | x + 1 3 5 | 2 x + 2 5

Question

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prove that

∣

∣

∣

∣

∣

∣

∣

∣

x+1

2

2

3

x+2

3

5

5

x+4

∣

∣

∣

∣

∣

∣

∣

∣

=(x−1)

2

(x+9)

Medium

Solution

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Δ=

∣

∣

∣

∣

∣

∣

∣

∣

x+1

2

2

3

x+2

3

5

5

x+4

∣

∣

∣

∣

∣

∣

∣

∣

C

1

+C

2

+C

3

Δ=

∣

∣

∣

∣

∣

∣

∣

∣

x+9

x+9

x+9

3

x+2

3

5

5

x+4

∣

∣

∣

∣

∣

∣

∣

∣

=(x+9)

∣

∣

∣

∣

∣

∣

∣

∣

1

1

1

3

x+2

3

5

5

x+4

∣

∣

∣

∣

∣

∣

∣

∣

R

2

=R

2

−R

1

R

3

=R

3

−R

1

Δ=(x+9)

∣

∣

∣

∣

∣

∣

∣

∣

1

0

0

3

x−1

0

5

0

x−1

∣

∣

∣

∣

∣

∣

∣

∣

expanding along C

1

we have

Δ=(x+9)×1

∣

∣

∣

∣

(x−1)

2

−0

∣

∣

∣

∣

=(x−1)

2

(x+9)