PLEASE USE MATLAB TO DO AND FILL OUT THE BLANK WITH ANSWERS. REMEMBER TO PRINT THE MATLAB CODE UNDERNEATH FOR THE CHALLENGE PROBLEM.

7. Determine: augmented matrix, rref equivalent form, and the solution, if any. 3x1x2+x3+2x4x1+2x2x3+x4x13x2+2x34x4=2=1=6 Augmented matrix: rref result: new equation from rref result: Number of pivots Free variables Solution type: Solution: Vector form of solution: p=,vh= Parametric form of solution: Challenge . Determine new equations, to add a 4th equation to the system of equations of problem 7, so that: a. the 4th equation leads to a new system of equations with a unique solution. b. the 4th equation leads to a new system of equations that is inconsistent. In each case write out the new system of equations and the equations from the rref result that illustrate the stated conditions. Print your MATLAB work to corroborate that your equations satisfy the stated conditions