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  3. 1 et a be the augmented matrix for a system...

Question: 1 et a be the augmented matrix for a system...

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1 et A be the augmented matrix for a system of four equations in four unknowns: xi, x, x and x Write down RREF(A) if the set of all solutions to the system of equations is ((5+s, 2-4t, s, t): t and s are real numbers) 2. The augmented matrix for a system of three equations in five unknowns has the following RREF 0 0 015 10 a) Find all solutions to the original system of equations. (Assume the five variables are xi, x. x.x b) If possible, find two particular solutions to the original system of equations for which x1-5. If it c) If possible, find two solutions for which x1-5 andx 2. If it is not possible, explain why not. 3. Consider the system of equations x3y +2z-a and xs.) Solutions should be written as 5-tuples. is not possible, explain why not. 2x+ 7y3 3x+ 10y-bz-4 where a and b are constants Find all possible conditions on a and b which will ensure that the system will have b) Find all possible conditions on a and b which will ensure that the system will have no solutions. cFind all possible conditions on a and b which will ensure that the system will have one unique (Note: To receive any credit, you must show your work. Your work must show how you reached infinitely many solutions. solution. 4. 2 3 6 Let AX1 be a system of equations. Suppose A- 4 13 a) Does the system of equations AX- have a solution? If so, find it. (Your answer must be exact. No decimal approximations will be accepted.) 86 4 If not, explain why not. b) State a theorem from the book that supports your answer
5 Let A be a 3x3 matrix and suppose that Y2 is a solution to the system of equations AX 5, and that Yo- 3 is a solution to the system AX- a) Find 3 additional non-zero solutions to the homogeneous system of equations AX-0 Show how you got these solutions b) Find 3 additional solutions to the system of equations AX5 Show how you got these solutions.
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