The Jacobian matrix of a set of variables is a matrix that represents the partial derivatives of functions. In this case, we are asked to find the Jacobian of p, q, r with respect to x, y, z given p=x+y+z, q=y+z, r=z.

The Jacobian matrix J is given by:

J = [ ∂p/∂x ∂p/∂y ∂p/∂z ]
[ ∂q/∂x ∂q/∂y ∂q/∂z ]
[ ∂r/∂x ∂r/∂y ∂r/∂z ]

We can calculate the partial derivatives as follows:

∂p/∂x = 1, ∂p/∂y = 1, ∂p/∂z = 1,
∂q/∂x = 0, ∂q/∂y = 1, ∂q/∂z = 1,
∂r/∂x = 0, ∂r/∂y = 0, ∂r/∂z = 1.

So, the Jacobian matrix is:

J = [ 1 1 1 ]
[ 0 1 1 ]
[ 0 0 1 ]

Question

The Jacobian matrix of a set of variables is a matrix that represents the partial derivatives of functions. In this case, we are asked to find the Jacobian of p, q, r with respect to x, y, z given p=x+y+z, q=y+z, r=z.

The Jacobian matrix J is given by:

J = [ ∂p/∂x  ∂p/∂y  ∂p/∂z ]
      [ ∂q/∂x  ∂q/∂y  ∂q/∂z ]
      [ ∂r/∂x  ∂r/∂y  ∂r/∂z ]

We can calculate the partial derivatives as follows:

∂p/∂x = 1, ∂p/∂y = 1, ∂p/∂z = 1,
∂q/∂x = 0, ∂q/∂y = 1, ∂q/∂z = 1,
∂r/∂x = 0, ∂r/∂y = 0, ∂r/∂z = 1.

So, the Jacobian matrix is:

J = [ 1  1  1 ]
      [ 0  1  1 ]
      [ 0  0  1 ]

Knowee AI · Accepted Answer

The Jacobian matrix of a set of variables is a matrix that represents the partial derivatives of functions. In this case, we are asked to find the Jacobian of p, q, r with respect to x, y, z given p=x+y+z, q=y+z, r=z.

The Jacobian matrix J is given by:

J = [ ∂p/∂x  ∂p/∂y  ∂p/∂z ]
      [ ∂q/∂x  ∂q/∂y  ∂q/∂z ]
      [ ∂r/∂x  ∂r/∂y  ∂r/∂z ]

We can calculate the partial derivatives as follows:

∂p/∂x = 1, ∂p/∂y = 1, ∂p/∂z = 1,
∂q/∂x = 0, ∂q/∂y = 1, ∂q/∂z = 1,
∂r/∂x = 0, ∂r/∂y = 0, ∂r/∂z = 1.

So, the Jacobian matrix is:

J = [ 1  1  1 ]
      [ 0  1  1 ]
      [ 0  0  1 ]

The Jacobian of p,q,r w.r.t x,y,z given p=x+y+z, q=y+z, r=z is ________Review Later021-2

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