Use Gaussian-Jordan eliminaltion to solve the linear system x₁ + x₂ + x3 + x₁ = 1 2x1 +4x2+6x3 + 8x4 x1 + 3x2 + 6x3 + 10x4 x1 +4x2+ 10x3 + 20x4 = 2 = 4 = 3

Find the minimum norm solution of the underdetermined linear system 2x₁ + x₂ + x3 + 5x4 = 8, -X₁ X₂ + 3x3 + 2x4 = 0.

5- Solve the system using the Gauss-Jordan elimination method: a- 3x1 +x2 - 2r3= 2 x1-2xz+ x3=3 2x1 - x2 - 3x3 = 3 b- 2x1 -x2 + 3x4 = 9 4x1 - 2x2 - 5x3= -10 3x1 + 5x2 + 2x3 -3x4= 0 -x2+x3-x4=-7

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).