\fProblem 4 Consider the following statements about a system of linear equations with augmented matrix A and coefficient matrix C. Prove that the statement is true, or give an example showing that it is false.\f\f\fProblem 2 Find the general solution of the homogeneous system of linear equations with the following matrix. {a} Carry the matrix to a reduced row echelon form using elementary row operations. For each step write the operation used. {h} Represent the general solution as a linear combination of basic solutions. For example, 1'1 -5 3 1'2 _ 1 1'3 1'2 2 + Id E :1." 1 Problem 1 Find the rank of the matrix by carrying it to a row echelon form.Problem 3 Find the general solution of the nonhomogeneous system of linear equations with the following augmented matrix. {a} Carry the augmented matrix to a reduced row eehelon form using elementary row operations. For each step write the operation used. (h} Represent the general solution as a sum of a particular solution of the nonhomogeneous system and a linear combination of basic solutions of the homogeneous system. For example 1'] 3 5 3 $3 1 d 2 1'3 = 2 + 113 1 'l' 11:5 3,; 4 2 7 $5 5 {l l