For the linear equation system given below 4x1 + 2x2 + 2x3 = 0 2x1 + 6x2 + 2x3 = 1 2x1 + 2x2 + 5x3 = 0
a) Write the system of linear equations in the form Ax = b. LU of matrix A obtained Find the decomposition using the Cholesky method.
b) Using the LU decomposition, find the solution of the system of equations given above.