Find a basis for and the dimension of the solution space of the homogeneous system of linear equations. X + 3y - 2z = 0 -4x - 12y + 8z = 0 (a) a basis for the solution space 3- (b) the dimension of the solution space

Find values of a, b, and c (if possible) such that the system of linear equations has a unique solution, no solution, and infinitely many solutions. (If not possible, enter IMPOSSIBLE.) = 6 z = 6 x+ y + z = 6 ax + by + cz = 0 (a) a unique solution -(C (а, b, с) %3D (b) no solution (а, b, с) %3D (c) infinitely many solutions -(C (a, b, c) =

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).

Solve the set of equations to vector form (a b c d)+lambda(e f g h)