state whether each fact is true or false if it is true explain why a f

Question

State whether each fact is true or false. If it is true, explain why (a full proof is not necessary, but your explanation should draw on concepts we learned from the course). Ifit is false, give a counterexample. If the answer is sometimes true, and sometimes false,depending on the values of the variables involved, then you should consider it to be false.For example, if I say: "Suppose A is 2 by 2. Then A² + A = 0." This fact is false, because there are values of A which do not satisfy that equation (for example, let A = I2). It should not be considered true just because setting A = 0 would make it true.On the other hand, if I say: 1. (4 marks) Suppose V is an inner product space, and W1, W2 are finite-dimensional subspaces of V. Suppose w E W1. Then