FP1 Homework Review

FP1 Homework

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: $$3\log2+4\log2^2+5\log{2^3}+....+(n+2)\log{2^n}$$