Homework 1: Systems of Linear Equations (Part 1)

1. Section 1.1, #1, 9(a).
2. Section 1.2, #2, 3(a), 5.
3. Row reduce matrix \(A\) to reduced row echelon form. List the pivot columns of \(A\). $$ A = \begin{bmatrix} 3 & 5 & 7 & 9 & 0\\ 2 & 6 & 10 & 14 & 0\\ 5 & 7 & 9 & 1 & 0 \end{bmatrix} $$
4. Find the equation \(y=ax^2+bx+c\) of the parabola passing through the points \((-2,-6)\), \((1,6)\), and \((3,4)\). (Your answer should be an equation of the form \(y=ax^2+bx+c\), for some constants \(a\), \(b\), and \(c\).)
   Hint: Substituting the \(x\)- and \(y\)-coordinates of a point into the equation \(y=ax^2+bx+c\) will produce a linear equation in \(a\), \(b\), and \(c\). Do this for the three given points to get three linear equations. Then solve the system of linear equations.