Mirror, Mirror, on the Wall. Let H be the plane 6x 3y 72 = 0, and L its normal line Span({( 6,3,7 )}). Find the matrices for projL, projn, and ren. Now, let? = (4, 5,2 ). Use your matrices to compute parojz> ), projn ), and ren). In your group, choose one person to go to geogebra.org The person will graph H, L, and the four vectors. Share your screen. Rotate the graph so that you get a diagram similar to that on p. 178. Once you do, take a screenshot, and share it with the other groupmates. Include the screenshot in your submission. 8. Playing with Operators. Let A = 4 2 a. Show the effect of A on the basis box in R2, including the effect on the letter "R" inside the box. Review the Example on p. 165. b. Compute p(A), where p(x) = -7x2 + 8x + 6. Explain what to do with "+6."Shear Operators A 2 x 2 Type 3 elementary matrix has the form: 6 "|o ' . 7 In the first case, the unit vector i is not affected, but T(j ) = ci + j, so the image of j is now leaning to the right or left, depending on whether c is positive or negative. Because of this, the first kind is called a horizontal shear operator. In the second case, j is not affected, but the image of i is now tilting up or down, so the second kind is called a vertical shear operator. Example: Let T be the operator with [7] - | -3/4 ]. Again, we see that T(i ) = i, T(j) =