Note: This is LInear Algebra question, so please make sure to answer it correctly

6. Perspective projections are used frequently in 3D graphics to simulate realistic view- points. In this problem, you will go through the process of taking a 3D object and projecting it to an image plane. (a) Derive the projection matrix for a 5 x 3 (w x h) image plane at z = 4 with the camera at (0,0,0) pointing down the z-axis. (b) Given the following coordinates of a cube, project the points of the cube onto the image plane using the projection matrix in part 1. [5 6 5 6 5 6 5 6] D = 0 0 1 1 0 0 1 1 7 7 7 7 6 6 6 6 (c) Plot the points as they would appear on the image plane. This will strictly be a 2D plot. Do not plot the points that would be occluded by visible faces of the cube. 6. Perspective projections are used frequently in 3D graphics to simulate realistic view- points. In this problem, you will go through the process of taking a 3D object and projecting it to an image plane. (a) Derive the projection matrix for a 5 x 3 (w x h) image plane at z = 4 with the camera at (0,0,0) pointing down the z-axis. (b) Given the following coordinates of a cube, project the points of the cube onto the image plane using the projection matrix in part 1. [5 6 5 6 5 6 5 6] D = 0 0 1 1 0 0 1 1 7 7 7 7 6 6 6 6 (c) Plot the points as they would appear on the image plane. This will strictly be a 2D plot. Do not plot the points that would be occluded by visible faces of the cube