please solve these problems.

Exercise 1: Use Gauss-Jordan elemination to solve the following systems (Show all steps) 0 09 -9 33 7 6 4 -1 5 -15 - 6 Exercise 2: Consider the following system of equations + + 2y - 2 =3, I- y = 2, 2x + y - 2 =5. 1. Write the system as an augmented matrix and perform some elementary row operations to make it in row reduced row echelon form. 2. What is the rank of the augmented matrix? How many free variables does this system have. 3. Write the solutions of the system in parametric form. 4. Consider the following system x + 2y - = =3, r- y = 2, 2xty - = =1. (The only difference is that 5 was replaced by 1). How would this change the RREF, the number of free variables and the solution set? Exercise 3: Let & be a real number. Consider the following system For which values of k (If there are any) does the system have 1. Infinitely many solutions. 2. Exactly one solution. 3. No solutions. Exercise 4: The intersection of the planes r + y + z = 1 and x + 2y + 2z = 1 is a line (This means that the system has infinitely many solutions). Find two vectors p, q such that the solutions can be written in parametric form as I y =p+t