Question: - 2 3. Let W = span( {v1, v2} ) where vi = V2 = Let WI O {VER' |V . W = OV WE

- 2 3. Let W = span( {v1, v2} ) where vi = V2 = Let WI O {VER' |V . W = OV WE W}. a) Prove that W and W- are subspaces of IR4. [2] b) Prove that if x E R' is a vector, then x E W- if and only if X . V1 = 0 and x . v2 = 0. [2] c) Using b) write down a system of 2 linear equations in 4 un- knowns x = (T1, 12, 13, 14) which determines whether x E R* is in WJ. [2] d) Find the general solution to your system in c). How many parameters does it have? Use your general solution to find a basis for WJ. [4]5. In the following question, Omxn refers to the zero m-by-n matrix. a) True or false: if A and B are 2-by-2 matrices such that AB = 02x2 then A = 0 or B = 0. Justify your answer by a proof if it is true, a counter-example if it is false. [2]

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