1.Find the inverse of $A=\begin{pmatrix}
\\1 & 3
\\4 & -1
\end{pmatrix}$
Use your answer to solve $x+3y=-2$ and $4x-y=5$
A triangle with area 5 is transformed using A, what is the area of the image of the triangle?
2. Find and simplify in terms of n\[\sum_{r=1}^{n} r(r+1)(r+2)\] Use this to find $\sum_{r=10}^{20} r(r+1)(r+2)$
3. \[S=\begin{pmatrix} \\0 & -1 \\-1 & 0 \end{pmatrix}\]S represents a linear transformation. Give a geometrical interpretation of S and show $S^2=I$. Give a geometrical interpretation of $S^{-1}$
4. Use the result \[\sum_{r=1}^{n}r(r+2)=\frac{n}{6}(n+1)(2n+7)\] to find: \[ 3\log2+4\log2^2+5\log{2^3}+....+(n+2)\log{2^n} \]
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