Prove that every permutation matrix is orthogonal

Math121 Chapter 3 Lesson 3.4 – Parallel and Perpendicular Lines EXAMPLE 1. 4x + 2y = 10 (First, we’re asked to put this in y = mx + b form.) 2y = -4x + 10 y = -2x + 5 (Now, we’re asked to find the equation for a line that is parallel to the line made by the linear equation we just got… and it runs through the point (8, 2). So, take the x and y from the point we were given, and…substitute it in to the linear equation we wrote. Remember, a parallel line means that it will have the exact same slope as the original line.) 2 = -2 (8) + b (Now, solve for b.) b = 18 (Now that we have b, we can substitute this into a new equation for the line parallel to the one in the original equation, using the same slope.) y = -2x + 18 (This is the linear equation to the line parallel to the original!) EXAMPLE 2. 2(y – 1) + ((4x + 5)/3) = -4 (First, we’re asked to put this in slope- intercept form, which is y = mx + b form. But we need to get y on a side by itself first, so…to get rid of the fraction,