Question

1
The jacobian of p,q,r w.r.t x,y,z
given p=x+y+z, q=y+z, r=z is *
(1 Point)​

Answer 1

Step-by-step explanation:

Explanation: We have to find

J = \frac{∂(p,q,r)}{∂(x,y,z)} = \begin{vmatrix} \frac{∂p}{∂x} & \frac{∂p}{∂y} &\frac{∂p}{∂z}\\ \frac{∂q}{∂x} &\frac{∂q}{∂y} &\frac{∂q}{∂z}\\ \frac{∂r}{∂x} &\frac{∂r}{∂y} &\frac{∂r}{∂z}\\ \end{vmatrix}

But p=x+y+z, q=y+z, r=z (taking partial derivative)

J=\begin{vmatrix} 1&1&1\\ 0&1&1\\ 0&0&1\\ \end{vmatrix}(\frac{∂p}{∂x}=1, \frac{∂p}{∂y}=1, \frac{∂p}{∂z}=1, \frac{∂q}{∂x}=0, \frac{∂q}{∂y}=1, \frac{∂q}{∂z}=1, \frac{∂r}{∂x}=0, \\ \frac{∂r}{∂y}=0, \frac{∂r}{∂z}=1)

On expanding we get

J = 1(1 – 0) = 1

Thus j = 1.