A nonlinear layer applies the map
f(x, y)=(x2y, 3x−y2)f(x,\ y) = \big(x^2 y,\ \ 3x - y^2\big)f(x, y)=(x2y, 3x−y2)
You are sitting at the point p=(2, 1)p = (2,\ 1)p=(2, 1) and take the small step
δ=[0.1−0.2]\delta = \begin{bmatrix} 0.1 \\ -0.2 \end{bmatrix}δ=[0.1−0.2]
Using the Jacobian JJJ of fff evaluated at ppp, what is the predicted change in the output, JδJ\deltaJδ?
Select all that apply.
[−0.20.8]\begin{bmatrix} -0.2 \\ 0.8 \end{bmatrix}[−0.20.8]
[−0.4−0.1]\begin{bmatrix} -0.4 \\ -0.1 \end{bmatrix}[−0.4−0.1]
[−0.40.7]\begin{bmatrix} -0.4 \\ 0.7 \end{bmatrix}[−0.40.7]
[0.21.1]\begin{bmatrix} 0.2 \\ 1.1 \end{bmatrix}[0.21.1]