Determine the kernel and range of each of the following linear operators in R3. a). L(x) = [x3 x2 x1], where x = [x1 x2 x3] b). L(x) = [x1 x1 x1], where x = [x1 x2 x3]
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Determine the kernel and range of each of the following linear operators in .
a).
![Determine the kernel and range of each of the following linear operators in R3. a). L(x) = [x3 x2 x1], where x = [x1 x2 x3] b). L(x) = [x1 x1 x1], where x = [x1 x2 x3]](https://www.doubtrix.com/uploads/editor/6189196568wjoCKkaWUU.jpeg)
![a). Compute the LU factorization of: A = [2 4 2 1 1 2 −1 0 2] b). Use the LU factorization to solve the system: Ax = [2 1 4], where x = [x1 x2 x3]](https://www.doubtrix.com/uploads/editor/3241516376UnRZSkFNdM.png)
![Write the solution set of the given homogeneous system in parametric vector form. 3x1 + 3x2 + 6x3 = 0 -9x1 - 9x2 - 18x3 = 0 -3x2 + 6x3 = 0 where the solution set is x = [x1 x2 x3]](https://www.doubtrix.com/js/ckeditor/filemanager/connectors/php/editor/1700962745-Q16.JPG)
![Describe the solutions of the first system of equations below in parametric vector form. Provide a geometric comparison with the solution set of the second system of equations below. 2x1 + 2x2 + 4x3 = 8 -6x1 - 6x2 - 12x3 = -24 -5x2 + 10x3 = 10 2x1 + 2x2 + 4x3 = 0 -6x1 - 6x2 - 12x3 = 0 -5x2 + 10x3 = 0 Describe the solution set, x = [x1 x2 x3] of the first system of equations in parametric vector form. Which option best compares the two systems? A. The solution set of the first system is a line parallel to the line that is the solution set of the second system. B. The solution set of the first system is a line perpendicular to the line that is the solution set of the second system. C. The solution set of the first system is a plane parallel to the plane that is the solution set of the second system. D. The solution set of the first system is a plane parallel to the line that is the solution set of the second system](https://www.doubtrix.com/js/ckeditor/filemanager/connectors/php/editor/1700963306-Q19.JPG)