Consider the following matrix. Assume that the matrix Is the augmented matrix of a system of linear equations. (a) Determine the number of equations and the number of variables. variables (b) Find the value(s) of & such that the system is consistent. OK - - OK- all real A / all real k = all real k Assume that the matrix is the coefficient matrix of a homogeneous system of linear equations. (a) Determine the number of equations and the number of variables. variables (b) Find the value(s) of & such that the system is consistent. OK - - OK- 7 all real k = all real k all real kSolve the system of linear equations. (Enter your answers as a comma-separated list. If there is no solution, enter NO SOLUTION. If the system has an infinite number of solutions, set X3 = t and solve for x, and x2 in terms of t.) 4X1 - 3X2 + 5X3 = 3 X1 + X2 - 3X3 = 4 3x1 - 4X2 + 8X3 = 9 (X1, X2, X3) =Find the value of k such that A i5 singular. (Enter your answers as a comma-separated list.)