1. Show that B = {A1, A2, A3} is a basis for U.
2. Any matrix of the form X^TX is symmetric. If X ? M₂(R) has columns u, v, i.e., X = u v , find [X^TX]B in terms of u u, v v, and u v

Let U = {A E M2(R) | AT = A}, and let A1 = (6 8) , 42 = ( 0 A3 = 0 : ) . (a) Show that B = {Al, A2, As} is a basis for U. (b) Any matrix of the form XX is symmetric. If X E M2 (R) has columns u, v, i.e., X = (u v), find [XX]B in terms of u . u, v . v, and u . v