You must show work to receive credit. RREF= reduced row echelon form. 1. (7pt) Solve the...

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You must show work to receive credit. RREF= reduced row echelon form. 1. (7pt) Solve the following systems of equations using the method of Gauss-Jordan Elimination (be sure to show your elimination steps) to convert the augmented matrix to RREF. Be sure to write the solution to the system (if there is one). Note: One solution will have fractions but not bad. Work these on a separate sheet. (a) (b) (c) 21 +22+3x3=8 3x1+7₂+9x3=26 2x1 +63=11 3x1+6x2 -324 3 ₁ +3x2-23-4x4--12 21-22 +23+24 = 8 2x+3x2 = 8 4x1 +82-12x3= 28 -21-2₂+ 3x3 = -7 2x1 +422-823= 16 -371-6x2+9r3=-21 2. (2pt) Solve the three systems of equations with the same coefficient matrix using Gauss-Jordan Elimination on a single larger augmented matrix. for each of the three vectors. 11 + 1₂ =b₁ 2x1+3x₂=b₂ Be sure to give the solution for each of the three vectors. = -BA 3. (2pt) Determine whether the vector (1,2) is a linear combination of the two vectors (1, 1) and (3,2). If it is, write it as linear combination, and if not, show how you know this. 4. (2pt) The following matrix is the RREF of an augmented matrix for a system of equations in the variables 300 03 6 00104 0001 5 -3 8 21,25. (a) Give the solution to this system and identify which of the variables are the free variables. (b) Choose specific values of the free variables to give three specific solutions to the system. 5. (2pt) There are infinitely many parabolas y = a + b + cr² that pass through the two points (x, y) = (1,3) and (x, y) = (4,9). Solve an appropriate system of equations using Gauss-Jordan Elimination (two equations and three variables) to find the equations of two parabolas (one that opens up and one that opens down) that contain the two points. That is, find all possible parabolas, and then (your choice)write the equations of two. You must show work to receive credit. RREF= reduced row echelon form. 1. (7pt) Solve the following systems of equations using the method of Gauss-Jordan Elimination (be sure to show your elimination steps) to convert the augmented matrix to RREF. Be sure to write the solution to the system (if there is one). Note: One solution will have fractions but not bad. Work these on a separate sheet. (a) (b) (c) 21 +22+3x3=8 3x1+7₂+9x3=26 2x1 +63=11 3x1+6x2 -324 3 ₁ +3x2-23-4x4--12 21-22 +23+24 = 8 2x+3x2 = 8 4x1 +82-12x3= 28 -21-2₂+ 3x3 = -7 2x1 +422-823= 16 -371-6x2+9r3=-21 2. (2pt) Solve the three systems of equations with the same coefficient matrix using Gauss-Jordan Elimination on a single larger augmented matrix. for each of the three vectors. 11 + 1₂ =b₁ 2x1+3x₂=b₂ Be sure to give the solution for each of the three vectors. = -BA 3. (2pt) Determine whether the vector (1,2) is a linear combination of the two vectors (1, 1) and (3,2). If it is, write it as linear combination, and if not, show how you know this. 4. (2pt) The following matrix is the RREF of an augmented matrix for a system of equations in the variables 300 03 6 00104 0001 5 -3 8 21,25. (a) Give the solution to this system and identify which of the variables are the free variables. (b) Choose specific values of the free variables to give three specific solutions to the system. 5. (2pt) There are infinitely many parabolas y = a + b + cr² that pass through the two points (x, y) = (1,3) and (x, y) = (4,9). Solve an appropriate system of equations using Gauss-Jordan Elimination (two equations and three variables) to find the equations of two parabolas (one that opens up and one that opens down) that contain the two points. That is, find all possible parabolas, and then (your choice)write the equations of two.