A system has "memory" if y(t₁) depends on u(t₁) as well as u(t), t>t₁. True False

A linear system with three equations and two variables must be inconsistent. True or false? Justify.  

mark 18. Consider the linear system Ax = b where A is a 5 x 5 invertible matrix. Which one of the following statements is false? A: There is a row of five zeroes in the row-reduced echelon form of A. | B: The rank of A is 5. C: The rank of Ab] is 5. D: The system Ax = b has a unique solution. E: The system Ax = 0 has only the trivial solution.

8. Determine if each of the following statements is true or false. Clearly indicate your answer for each part by stating if it is true or false no justification is required). Each part is worth 2 marks for a correct answer; -1 for an incorrect answer to discourage guessing) (a) If A and B are n x n matrices, then rank(BA) rank(A). (b) If {A, B, C} is a linearly independent set of n x m matrices, then {AT, BT,CT} is a linearly independent set of m x n matrices. (C) W = {A E Rnxn A is invertible } is a subspace of Rnxn, where Rnxn denotes the vector space of real n x n matrices. (d) If xi and X2 are orthogonal vectors in R3 then it is always possible to find a unique vector X3 such that {x1, X2, X3} is an orthogonal basis for R3. (e) Let W be a subspace of R" and let x ER". Then projw(x - projw(x)) = 0.