must solve ALL parts for upvote No solutionsUnique solution: x = -4, y = -1Infinitely many solutionsUnique solution: x = 0, y = -4Unique solution: x = 0, y = -4, z = -1None of the aboveF0 00Unique solution: x = 0, y = 0Unique solution: x = 0, y = 0, z = 0Infinitely many solutionsNo solutionsUnique solution: x = 1, y = 1, z = 0None of the above[1 00-301 0-3L00 0 0Unique solution:x = -3, y=-3None of the aboveInfinitely many solutionsUnique solution: a = -3, y = -3Unique solution: x = 0, y = 0, z = 0No solutions0 04[4]0 1 0-10 0 0-1No solutionsUnique solution: x = 4, y = -1Unique solution: x = 4, y = -1, z = -1Infinitely many solutionsUnique solution: x = 4, y = -1, z = 0None of the above Solve the following system using augmented matrix methods:2x12x2 - 4x3 = 285x1+3x21x3 = 410x16x22x3 = 6(a) The initial matrix is:9(b) First, perform the Row Operation R₁ → R₁. The resulting matrix is:9.(c) Next, perform the operations-5R₁ + R₂R₂-10R₁ + R3The resulting matrix is:R3.9.(d) Finish simplifying the augmented matrix down to reduced row echelon form. Thereduced matrix is:(f) What are the solutions to the system?Remember: This matrix must be simplified all the way to reduced form.(e) How many solutions does the system have? If infinitely many, enter "Infinity".*1 =9.x₂ =1x3 =

We have to solve the equation of the system using reduced echelon form. and find required values

Solve the following system using augmented matrix methods: 2x12x2 - 4x3 = 28 5x1+3x21x3 = 4 10x1+6x22x3 = 6 (a) The initial matrix is: 9. (b) First, perform the Row Operation R₁ → R₁. The resulting matrix is: (c) Next, perform the operations -5R₁ + R₂ R₂ -10R₁+R3 R3. The resulting matrix is: 9. (f) What are the solutions to the system? 9. x1 = 9. 9. 9. (d) Finish simplifying the augmented matrix down to reduced row echelon form. The reduced matrix is: 4 9. Remember: This matrix must be simplified all the way to reduced form. (e) How many solutions does the system have? If infinitely many, enter "Infinity". 9.