3. (20 points) (Computer problem) Write a computer program that solves a linear system with a tri-diagonal matrix. a1 bi 0 0 C1 a2 b2 0 C2 03 b3 : An-1 bn-1 Cn-2 0 0 Cn-1 An Use the Gaussian elimination that follows the band structure. Test your code on the 100 x 100 matrix, -1 X 1 X2 1 0 -1 A= -1 2 -1 X 100 Show the first 5 entries of the solution vector. 3. (20 points) (Computer problem) Write a computer program that solves a linear system with a tri-diagonal matrix. a1 bi 0 0 C1 a2 b2 0 C2 03 b3 : An-1 bn-1 Cn-2 0 0 Cn-1 An Use the Gaussian elimination that follows the band structure. Test your code on the 100 x 100 matrix, -1 X 1 X2 1 0 -1 A= -1 2 -1 X 100 Show the first 5 entries of the solution vector