Let A = 1 1 1 1 0 1 1 1 0 0 1 1 0 0 0 1 , b = 5.00 1.02 1.04 1.10 An approximate solution of Ax = b is calculated by rounding the entries of b to the nearest integer and then solving the rounded system with integer arithmetic. The calculated solution is x_ = (12, 4, 2, 1)T . Let r denote the residual vector. (a) Determine the values of _r_ and cond(A). (b) Use your answer to part (a) to find an upper bound for the relative error in the solution. (c) Compute the exact solution x and determine the relative error _x x__ _x_ . 3

2.2 Linear equations are one variable 2x-3=0 is a linear equation in one variable Linear equation with two variables 2y+2x=0 Such an equation represents a line How do we find equation for a line Given two points (1,8) (0,1) on a line. Find an equation. Y-y1=m(x-x1) to change to slope intercept distribute slope and add y sub one value to equation. How can you tell the relationship between two lines The two lines can be parallel or perpendicular. Set equations equal to one another. Y=1/2x-1 Y=x+1 To find x then substitute x value into original equation. 2.4 Complex Numbers I=sqrt of -1 2=2+0i