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Find the derivative, r'(t), of the vector function. r(t)=e^(t^2)i-j+ln(1+3t)k

The main purpose of this question is to find the derivative of a given vector-valued function. A vector function accepts one or perhaps many variables and yields a vector. Computer graphics, computer vision,  and machine learning algorithms frequently use vector-valued functions. They are especially helpful for determining space curve parametric equations. It is a function possessing two characteristics such as […]

Determine whether the given set S is a subspace of the vector space V.

$V=P_5$,  and $S$ is the subset of $P_5$ consisting of the polynomials satisfying $p(1)>p(0)$. $V=R_3$,  and $S$ is the set of vectors $(x_1,x_2,x_3)$ in $V$ satisfying  $x_1-6x_2+x_3=5$. $V=R^n$ and $S$ is a set of solutions to the homogeneous linear system $Ax=0$, where $A$ is a fixed $mtimes n$ matrix. $V=C^2(I)$, and $S$ is the subset […]