Note the higher point value. 1. Consider the system of linear equations 2w+6y =2 3y+3z =6 m+y+z :1 (a) [7 points] Explicitly give the augmented matrix associated to this system, where the variables are ordered left-to-right as :r, y, z. (b) [7 points] After a sequence of elementary row operations performed on the aug- mented matrix, one obtains 1 0 O 1 0 1 0 0 0 0 1 2 What is the solution set of the original system? 2. [8 points] Consider a system of three equations in two unknowns represented by the following plot. Given that information, which of the following augmented matrices is most likely row equivalent to the augmented matrix associated to the original system? Justify your answer in complete sentences. A. 100 010 000 B. 100 010 001 C. 100 000 000 3. [7 points] Give an example of a homogeneous system of linear equations. 4. Let E E R100 be a unit vector. (a) [7 points] Give (with justication) the explicit value of ]|5E||. (b) [7 points] If 1100 is the 100 x 100 identity matrix, then what is the explicit value of \"110055\"? Justify your answer. (0) [7 points] If 0100 is the 100 x 100 zero matrix, then what is the explicit value of ||0100E||? Justify your answer. (d) [7 points] Give (with justication) the explicit value of (E, E). (e) [7 points] How many rows and columns does ET have? 11 2 0 A=(01) and B=(0 _3). (a) [6 points] Explicitly compute A + B. 5. Let (b) [6 points] Explicitly compute AB. (c) [6 points] Explicitly compute BA