KnowledgeBoat Logo
|

Mathematics

If [x+yxy]=[84]\begin{bmatrix} x + y \ x - y \end{bmatrix} = \begin{bmatrix} 8 \ 4 \end{bmatrix}, then the value of xy is:

  1. 4

  2. 8

  3. 10

  4. 12

Matrices

1 Like

Answer

Given,

[x+yxy]=[84]\begin{bmatrix} x + y \ x - y \end{bmatrix} = \begin{bmatrix} 8 \ 4 \end{bmatrix}

∴ x + y = 8 …..(1)

∴ x - y = 4 …..(2)

Adding equations (1) and (2), we get :

⇒ x + y + x - y = 8 + 4

⇒ 2x = 12

⇒ x = 122\dfrac{12}{2}

⇒ x = 6.

Substituting value of x in equation (1) :

⇒ x + y = 8

⇒ 6 + y = 8

⇒ y = 8 - 6

⇒ y = 2.

∴ xy = 6 × 2 = 12.

Hence, option 4 is the correct option.

Answered By

3 Likes


Related Questions