Question

Question from determinant !

Plz solve it ✌✌​

Answer 1

• In this question, we use the properties of determinant.

And after solving

• Expand the determinant .

Solution refer to the attachment

Answer 2

Step-by-step explanation:

Given,

$\left[\begin{array}{ccc}y+z&z&y\\z&z+x&x\\y&x&x + y\end{array}\right]$

C₁ -> C₁ + C₂ + C₃

$\Rightarrow \left[\begin{array}{ccc}2(y+z)&z&y\\2(z+x)&z+x&x\\2(y+x)&x&x + y\end{array}\right]$

$\Rightarrow 2\left[\begin{array}{ccc}(y+z)&z&y\\(z+x)&z+x&x\\(y+x)&x&x + y\end{array}\right]$

C₁ -> C₁ - C₂

$\Rightarrow 2\left[\begin{array}{ccc}y&z&y\\0&z+x&x\\y&x&x + y\end{array}\right]$

C₃ -> C₃ - C₁

$\Rightarrow 2\left[\begin{array}{ccc}y&z&0\\0&z+x&x\\y&x&x\end{array}\right]$

R₃ -> R₃ - R₁

$\Rightarrow 2\left[\begin{array}{ccc}y&z&0\\0&z+x&x\\0&x-z&x\end{array}\right]$

⇒ 2y[(z + x)x - x(x - z)]

⇒ 2y[2xz]

⇒ 4xyz

Hope it helps!