Solving a system of three linear equations in 3 unknowns using Gauss Elimination in 4 stages. Solutions are all integral.

Express $\displaystyle \frac{a}{(x+r)(px + b)} + \frac{c}{(x+r)(qx + d)}$ as an algebraic single fraction over a common denominator. The question asks for a solution which has denominator $(x+r)(px+b)(qx+d)$.

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Solving a system of three linear equations in 3 unknowns using Gauss Elimination in 4 stages. Solutions are all integral.

Find the determinant and inverse of three $2 \times 2$ invertible matrices.

Given a codeword in $w=\mathbb{Z}^4_3$ find and list all codewords at Hamming distance $1$ from $w$.

Split $\displaystyle \frac{ax+b}{(cx + d)(px+q)}$ into partial fractions.

Split $\displaystyle \frac{b}{(cx + d)(px+q)}$ into partial fractions.

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$I$ compact interval, $g:I\rightarrow I,\;g(x)=ax^3+bx^2+cx+d$. Find stationary points, local and global maxima and minima of $g$ on $I$

$I$ compact interval, $g:I\rightarrow I$, $g(x)=(x-a)(x-b)^2$. Stationary points in interval. Find local and global maxima and minima of $g$ on $I$. 

$g: \mathbb{R} \rightarrow \mathbb{R}, g(x)=\frac{ax}{x^2+b^2}$. Find stationary points and local maxima, minima. Using limits, has $g$ a global max, min? 

$I$ compact interval. $\displaystyle g: I \rightarrow I, g(x)=\frac{ax}{x^2+b^2}$. Find stationary points and local maxima, minima. Using limits, has $g$ a global max, min? 

$I$ compact interval. $\displaystyle g: I\rightarrow I, g(x)=\frac{x^2}{(x-c)^{a/b}}$. Are there stationary points and local maxima, minima? Has $g$ a global max, global min? 

$I$ compact interval, $g:I\rightarrow I,\;g(x)=ax^3+bx^2+cx+d$. Find stationary points, local and global maxima and minima of $g$ on $I$

$I$ compact interval, $g:I\rightarrow I$, $g(x)=(x-a)(x-b)^2$. Stationary points in interval. Find local and global maxima and minima of $g$ on $I$. 

$I$ compact interval. $\displaystyle g: I\rightarrow I, g(x)=\frac{x^2}{(x-c)^{a/b}}$. Are there stationary points and local maxima, minima? Has $g$ a global max, global min? 

Split $\displaystyle \frac{b}{(cx + d)(px+q)}$ into partial fractions.

Solving a system of three linear equations in 3 unknowns using Gauss Elimination in 4 stages. Solutions are all integral.

Find the critical point  $(0,a)$ of the function: $f(x,y)=ax^3+bx^2y+cy^2+dy+f$ and find its type using the test given by the Hessian matrix.

Find the determinant and inverse of three $2 \times 2$ invertible matrices.

Find the determinant and inverse of three $2 \times 2$ invertible matrices.