2a 4 Span{-0} (a) Determine all real values a and b such that in R². (b) Determine the solution set, S, to the following system of linear equations. 1 +3r2 I1 +3r2 -zs +3r4 = 0* +4z4 = 0 Express S as the span of one or more vectors.

Suppose you want to interpolate the points (−1, 0), (0, 6), (1, 0) and (2, 0) by a polynomial. (a) What will the degree of the interpolating polynomial be? Write down the linear system. Solve the system to get the polynomial. Find the interpolated value at t = 1/2. (b) Write down directly the Lagrange basis interpolation. Simplify the polynomial to get the same answer as (a).

Consider the system of equations 2x + 4y = -2 -x+3y = 6 (a) Write down the tabular form of this system of equations. (b) Using row operations find the exact answer for (x, y). Make sure you show intermediate steps You must conta

Give all solutions of the nonlinear system of equations, including those with nonreal complex components. 71) x2 + y2 = 113 x -y =1 A) {(-8, -7), (-7, -8)} C) {(8,7), (-7,-8)} 71) %3! B) {(8, -7), (7, -8)} D) {(-8,7), (-7,8)}