-3 + y %3D Consider the homogeneous lincar system. 2r - 2y (a) Write the system in matrix-vector form. (b) Then, check to see if either of the following vector-valued functions is a solution to the system. x(t) : 2e-t

please show all work   2.    Consider a linear system below:2x − y + z = 2 x + 2y − z = 53x + y + 2z = 5 (a)    For the system above, write the coefficient matrix and the solution vector     (b)    Solve the system using Gauss-Jordan method. Classify your answer.     (c)    Find the inverse of the coefficient matrix you found in part a), then multiply it by the solution vector. What do you notice? Prove that the matrix you found is in fact an inverse.

Describe and compare the solution sets of x₁ +5x₂ - 2x3 = 0 and x₁ + 5x₂ - 2x3 = -7. X1 E Describe the solution set, x= x₂ of x₁ +5x₂ - 2x3 = 0 in parametric vector form. Select the correct choice below and fill in the answer boxes within your choice. X3 (Type an integer or fraction for each matrix element.) OA. X= O B. X=X3 C. X=X₂ O D. X= + X3 X1 E x2 of x₁ + 5x₂ - 2x3 = = -7 in parametric vector form. Select the correct choice below and fill in the answer boxes within your choice. x3 (Type an integer or fraction for each matrix element.) OA. X= B. X= +X₂ Describe the solution set, x = O c. x= O D. X=X₂ +X3 +x₂ + X3 +X3 Which option best compares the two equations? O A. The solution set of the second equation is a plane perpendicular to the line that is the solution set of the first equation. O B. The solution set of the second equation is a plane parallel to the plane that is the solution set of the first equation. OC. The solution set of the second equation is a plane parallel to…

Use an inverse matrix to solve each system of linear equations. (a) x + 2y = -1 x - 2y = 3 (x, y) = = (1 (b) x + 2y = 11 x - 2y = -5 (x, y) = (1