⌈1 0⌉⌈x⌉=⌈ x⌉
The above 2x2 matrix reflects a point over the x-axis. (x,y)→(x,-y).
Derive a matrix that will reflect a point over the line y=kx.
Mr and Mrs Brown are a little strange. When they are awake, their judgement about everything is absolutely perfect. When they are asleep however, it is exactly the opposite.
That is, if Mr Brown is awake and thinks that something is true, then it will always be true. But if he were to be sleeping and dreaming something to be true, it would always turn out to be false.
Once, late at night, Mr Brown was under the impression that Mrs Brown is asleep. At that very point in time, Mrs Brown was also thinking about her husband. Was she under the impression that he was asleep or that he was awake?