Please solve full question step by step.

CO1: Use computational techniques and algebraic skills essential for the study of systems of linear equations, matrix algebra, linear combination and Apply Matrices and inverse matrices for coding and encrypting messages. 1. a) Test for consistency and if consistent then find the solution for the system of equations: x+y+z=3, 2x+ y-z = 2, 4x -y+2z =5 [5] b) Find the general flow pattern of the network shown in the figure. Assuming that the flows are all nonnegative, what is the largest possible value for x3? [5] 20- 80 2. a 3 3 0 3 Find the rank of the matrix A - 7 52 [4] 2 3 1] b) Using A- to decode the following Cryptogram A = 1, 25, -65, 17,15, -9, 12, -62, 119,27,51,48,43,67,48,57,111,117 [6] 3. a) |Express the vector (4, 5, 5) as a linear combination of the vectors (1, 2, 3), (-1, 1, 4) and [4] (3, 3, 2). What are the most popular applications of eigenvalues and eigenvectors in practical terms. in fields such as computer science and computer graphics? Find the Eigen values and eigen 3 2 [6] vectors of matrix A =