Question

1. The Jacobian of p, q,r w.r.t

x, y, z given

p = x +y +z, x = y + z, r = z is

O 2

0 1

0 -1​

Answer 1

Answer:

0 -1 answer. I can't explain

Answer 2

SOLUTION

TO CHOOSE THE CORRECT OPTION

The Jacobian of p , q , r w.r.t x, y, z given

p = x + y + z , q = y + z , r = z is

• 2

• 1

• - 1

CONCEPT TO BE IMPLEMENTED

If p , q , r are three functions of x , y , z then their Jacobian is

$\displaystyle \sf{ = \frac{ \partial (p,q,r)}{ \partial (x,y,z)} }$

$= \displaystyle \begin{vmatrix} \frac{ \partial p}{ \partial x} & \frac{ \partial p}{ \partial y} & \frac{ \partial p}{ \partial z}\\ \\ \frac{ \partial q}{ \partial x} & \frac{ \partial q}{ \partial y} & \frac{ \partial q}{ \partial z} \\ \\ \frac{ \partial r}{ \partial x} & \frac{ \partial r}{ \partial y} & \frac{ \partial r}{ \partial z} \end{vmatrix}$

EVALUATION

Here it is given that

p , q , r are three functions of x , y , z

Now

p = x + y + z , q = y + z , r = z

Now the Jacobian

$\displaystyle \sf{ = \frac{ \partial (p,q,r)}{ \partial (x,y,z)} }$

$= \displaystyle \begin{vmatrix} 1 & 1 & 1\\ \\ 0 & 1 & 1 \\ \\ 0 & 0 & 1 \end{vmatrix}$

$= 1 + 0 + 0$

$= 1$

FINAL ANSWER

Hence the required Jacobian = 1

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