Answer question 1 a-t and 2 a-c

Question 1 (15 points): Consider the following system of equations: 4x + 12y - 19z = 2 6x - 13z = -4 7x - 6y - 10z = -7 a) (1 point) Write down this system as an augmented matrix b) (6 points) Using elementary row operation, transform the matrix into its Reduced Row Echelon Form. SHOW YOUR WORK (i.e., show each elementary row operation that you perform) and have all numbers as simple ratios (i.e., p/q where p and q have no common factors), not decimals! c) (2 points) Write down all solutions to this system of equations Now, assume we add another equation to the system: a - x + 36y - 5z = b, where a and b are some constants. So, we have a system of 4 equations with 3 unknowns d) (2 points) For which values a and b the new system has an infinite number of solutions? If there are no such values, prove it. e) (2 points) For which values a and b the new system has exactly one solution? If there are no such values, prove it. e) (2 points) For which values a and b the new system has no solutions? If there are no such values, prove it. Question 2 (5 points): Let A = 0 3 and B - [ 9, 6] a) (1 point) Find AT b) (3 points) Does AB exist? If it does, find it (show your work!) c) (1 point) Does BA exist? If it does, find it (show your work!)