(1) Using the matrices and vectors below, solve for the following quantities. For any matrix-vector multiplica- tion, show your response as a linear combination using vector equations. If an expression is malformed (cannot be solved) you must explain precisely Why it cannot be resolved. 2 0 1 1 2 0 a a A=71724 3:132 596 132 '222 0:748 4 4 8 4 1 l_ 2 1 a: 0 y' 3 2: 6 2 1 6 (a)AB (b)BTC (a)??? MM??? (e)Ai (f) 0T1? ' \"'"\"'\"'\\\"J' "\"'\"'\"\" "\"'""' \""\"\"\"""J \\-'. l""""'"l | 3 4 3 4 before performing the matrix multiplication, which performs each of the transformations described in the order given. Hint: scaling and then rotating is not necessarily the same thing as rotating and then scaling. (2) Provide a nal expression for the transform A, as well as A in it's factored form (e.g. A = CB = [1 2] [1 2]) E For the rotation matrix in factored form, do not evaluate any trigonometric functions (eg. leave cos (2) in your matrix instead of D). You may use unit vectors (when possible) to verify your nal transform, but answers Without the factored form will not receive full credit. 0 quadruple the magnitude of 2:0 and quarter the magnitude of 3:1. I rotate 45 degrees counter-clockwise about the origin. 5'30 (b) Let 5.5: :51 e R3 332 a double the length of if. 9 rotate 90 degrees around the positive 3:2 axis. (c) Let E E R2 a swap the 9:0 and 3:1 coordinates. o rotate 30 degrees counter-clockwise about the origin. (d) Let i" =6 R2 o rotate 60 degrees clockwise about the origin. 0 discard the second dimension (leaving a vector with only one entry). Note: you may need to think critically about this step and how to achieve it on it's own. (3) Let: 0 2 U U 0 U 2 U A_ 0 U U 2 0 U U U W Compute each of the following where f = :1 . 2 El (a) An? (b) AAIE (c) AAALE' ((1) Describe, in a sentence or two, the action of left-multiplying a vector is" by A as Azi. H Spans (10 points) (4) Find the span for each of the following sets of vectors. Be sure to: o Write out a vector equation that describes the span o Describe in words the shape of the span; be more specic than simply \"a line" or \"a plane\". (a) a: [g] and a: [2\"] 7T