Matrix Calculus

Practice Questions

Linear Algebra › Matrix Calculus

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Give the Hessian matrix for the function $f(x,y) = xy^{2}e^{x}$ .

Find the Hessian of the following function.

$f(x,y,z)=\frac{1}{2}xy^2+\ln(yz^2)+x^3$

$\begin{align*}&\text{Approximate }\begin{bmatrix}x\y\end{bmatrix}\&\text{for the system: }\begin{bmatrix}-12&9\13&14\-5&-16\end{bmatrix}\begin{bmatrix}x\y\end{bmatrix}=\begin{bmatrix}-100\-5\14\end{bmatrix}\end{align*}$

Give the Hessian matrix for the function $f(x,y) = xy^{2}e^{x}$ .

Find the Hessian of the following function.

$f(x,y,z)=\frac{1}{2}xy^2+\ln(yz^2)+x^3$

$\begin{align*}&\text{Calculate the gradient of the function}\&f(x,y,z)=-9xsin(6y)e^{(3z)}\end{align*}$

$\begin{align*}&\text{Calculate the Hessian matrix of the function}\&f(x,y)=2cos(2x)cos(5y) + 6\cdot 2^{(6x)}tan(4y)\end{align*}$

$\begin{align*}&\text{Determine the Hessian, }H\text{, of the function}\&f(x,y)=20xy^{2}\end{align*}$

$\begin{align*}&\text{Calculate the gradient of the function}\&f(x,y)=4ycos(5x) - 13ln(3y)sin(3x)\end{align*}$

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