(70 pts) Given matrices A=13 2 4 2 8 11 and B=1-6 2. 1 a) (20 pts) please illustrate three ways (i.e. dot product, column operation, and row operation) to compute for A * B = C calculation. Please show your work and also show the result of C. (note: You are not to use any MATLAB commands.) b) (50 pts) an elementary matrix is a matrix which differs from the identity matrix by one single elementary row operation. For example, o 1 is an elementary matrix. Elimination matrices are elementary matrices that can multiply an invertible matrix into an upper triangular matrix. For example, the matrix 2 4 21 8 L0 4 1 A = 13 1 | can be multiplied into an upper triangular matrix with pivoting by 2 4 21 [3 8 1 0 4 1 l0 0 5/3 where E32, E31 and E21are three elementary elimination matrices and P23 and P1z are permutation matrices that swap rows. Please define the three elimination matrices E32, E31 and E21and the two permutation matrices P23 and P12. Please show your work by finding Po2, E21, E31, P23 and E32 in sequence and in that order. Please compute the Determinant of the matrix A using the resulting upper triangular matrix. Please find the solution vector x2 using the result for the linear system below: 2 4 211X11 [16 0 4 11X3] 11