Question

urgent please !!!!!!​

Answer 1

Question:

Find the value of determinant

3 - 4 5

1 1 - 2

2 3 1

Answer:

The value of the determinant is 46.

Option A) 46

Step-by-step-explanation:

The given determinant is

3 - 4 5

1 1 - 2

2 3 1

Let this determinant be A.

By applying row transformation R₁ → R₁ - ( R₂ + R₃ )

⇒ A = 3 - ( 1 + 2 ) - 4 - ( 1 + 3 ) 5 - ( - 2 + 1 )

1 1 - 2

2 3 1

⇒ A = 3 - 3 - 4 - 4 5 + 1

1 1 - 2

2 3 1

⇒ A = 0 - 8 6

1 1 - 2

2 3 1

By applying row transformation R₃ → R₃ - R₂

⇒ A = 0 - 8 6

1 1 - 2

2 - 1 3 - 1 1 - ( - 2 )

⇒ A = 0 - 8 6

1 1 - 2

1 2 1 + 2

⇒ A = 0 - 8 6

1 1 - 2

1 2 3

By expanding the determination along first column,

A = 0 * D₁ - 1 * D₂ + 1 * D₃

⇒ A = 0 - D₂ + D₃

⇒ A = D₃ - D₂

Where,

D₂ = - 8 6

2 3

⇒ D₂ = ( - 8 * 3 ) - ( 6 * 2 )

⇒ D₂ = - 24 - 12

⇒ D₂ = - 36

And,

D₃ = - 8 6

1 - 2

⇒ D₃ = [ - 8 * ( - 2 ) ] - ( 6 * 1 )

⇒ D₃ = 16 - 6

⇒ D₃ = 10

Now,

A = D₃ - D₂

⇒ A = 10 - ( - 36 )

⇒ A = 10 + 36

⇒ A = 46

∴ The value of the determinant is 46.