1 Let u = 2 and v = . Let P = span {u, v}. Find an equation for the plane P. 2 In this question we introduce a new definition. Definition: Let T : R" - R" be a linear transformation. We say that x E R" is a resting point of T if T(x) = x. Additionally, we say that T is restless if the only fixed point of T is x = 0. Which of the following linear transformations RR2 - R2 are restless? Make sure to justify your answer (if a given transformation is restless, you should explain why no x * 0 can be a resting point; if a given transformation is not restless, you should give an example x * 0 which is a resting point for T.) 2.1 Q given by stretching horizontally by a factor of 2, and vertically by a factor of 3. 2.2 R given by counterclockwise rotation by It / 4. 2.3 S given by the matrix As = 2.4 T given by reflection across the line y = x.P 5 _./J N - ) W 3.4 Determine if the statements below are True or False. If it's True, explain why. If it's False explain why not, or give an example demonstrating why it's false with an explanation. A correct choice of \"True\" or \"False\" with no explanation will not receive any credit. True or False: If {x,y} and {z, w} are both linearly independent sets in IR\