5. For each of the statements given below decide if it is true or false. If it is true explain why. If it is false give a counterexample. a) If A, B are matrices such that AB is defined and is a square matrix (i.e. it has the same number of rows and columns) then BA is also defined. b) If A is an 2 x 2 matrix such that Av = 0 for some non-zero vector v € R² then A cannot be invertible. c) If {V₁, V₂} is a linearly independent set of vectors in R2 and T: R² →→>> R² is a linear transformation then the set {T(v₁), T(v₂)} must be also linearly independent. d) If u, v, w are vectors in R² such that u is in Span(v, w) then v must be in Span(u, w).

Let x=(4,3, 1, 1) and y (8, 2, 7, 1). Determine which of the following statement(s) is/are true: (i) xy is a scalar (ii) xy" is a matrix (iii) yx is a matrix (iv) xyx is a vector O a. (ii), (i) and (iv) only O b. (i), (ii) and (iv) only Oc. All of the above O d. (i), (ii) and (iii) only.

If B non singular 2 x 2 matrices and k is a non zero scalar . Which one of the following expressions is correct