Let $p(x)$ be a monic polynomial of degree 6 such that $p(1) = 1,$ $p(2) = 2,$ $p(3) = 3,$ $p(4) = 4,$ $p(5) = 5,$ and $p(6) = 6.$ Find $p(7).$
awesome! I got the six equations and six unknowns but was intimidated to solve it.
"I got the six equations and six unknowns but was intimidated to solve it."
I'm not surprised. I wouldn't have bothered if I didn't have software available to do it! Although there is a matrix capability on the web2.0 calculator on the home page here, it just goes up to 4x4 matrices, so wouldn't have helped here. Probably Wolfram Alpha would do it, but I haven't tried it with this problem.