Numerical AnalysisPlease show all the steps. Question(a)(b)We are given four data points:(c)Here is an uncompleted divided difference matrix:3(1,3)7(3,7)0f[0, 1]9[1, ₂] [10, 11, 12]27 f[2,3] [1, 2, 3] [10, 11, 12, 13].,Complete the matrix.divided difference formula:0(4,9)0(10, 27).000Hence write down the Lagrange interpolating polynomial on the full data set, here is theP(x) = f[ro] + f[0, T₁] (T-TO) +ƒ[TO, E₁, E2] (x− I0) (x − E₁)+ƒ[10, 11, 12, 13] (1−10) (T—F₁) (T-T₂).Give one difference between Lagrange and Hermite interpolating polynomials.

The divide difference table as shown below:

Question (a) (b) We are given four data points: (c) Here is an uncompleted divided difference matrix: 3 7 (1,3) (3,7) 9 27 Complete the matrix. divided difference formula: 0 f[0, 1] f1, ₂] [TO, I1, I2] 0 f[2,3] [1, 2, 3] [10, 11, 12, 13]., 0 (4,9) 0 (10, 27). 0 0 Hence write down the Lagrange interpolating polynomial on the full data set, here is the P(x) = f[ro] + f[ro, #1] (T−TO) +ƒ [TO, T1, T2] (T−TO) (T-T1) + ƒ [TO, T1, T2, T3] (T-TO) (T-T1)(x − T2). Give one difference between Lagrange and Hermite interpolating polynomials.