To obtain the matrix in reduced row-echelon form, apply elementary row operations until every column thathas a leading 1 has zeros in every position above and below its leading 1.Perform the operations (R2AR:)on R2 and (R3on R3.9R111.1-2-2 -3 V-3 :R2 - 4R1R3 - 9R10 -6: 12-812Step 2Perform the operation (-R2) on R2.1.1-23: -5/21.20 -6 -8:12Perform the operation (R3 + 6R2)1 11:-230 1R3 + 6R20 0 1: Use a system of equations to find the quadratic function f(x) = ax2 + bx + c that satisfies the equations.Solve the system using matrices.f(1) = -2, f(2) = -3, f(3) = -6Step 1The given quadratic function is f(x) = ax? + bx + c.It is given that f(1) = -2, f(2) = -3, and f(3) = -6.Substitute x = 1, x = 2, and x = 3 into f(x) = ax2 + bx + c to form the system of linear equations.%3Df(1) = a + b + c = -2f(2)= 4a + 2b + c = -3f(3) = 9a + 3b + c = -6a + b + c = -2Therefore, the obtained system of equations is {4a + 2b + c = -3.9а + 3b + с %3D -6Write the associated augmented matrix for this system.1 1 1: -24 2 1: -39 3 1: -6

Given: To determine: Matrix after operation R3+6R2

To obtain the matrix in reduced row-echelon form, apply elementary row operations until every column that has a leading 1 has zeros in every position above and below its leading 1. Perform the operations (R2 - 4R1) on R2 and (R3 - 9R1) on R3. 1 1 0 -2 -3 -2 -3 : 5 5 R2 - 4R1 → R3 - 9R1 → 0 -6 : 12 V -8 12 step 2 Perform the operation (-R2) on R2. 1 -2 0 1 3 : -5/2 V 2 0 -6 -8 : 12 Perform the operation (R3 + 6R2) on R3. 1 1 3 0 1 2 R3 + 6R2 0 0 1 ... .. 1.