2 Let T Rm Rn be a linear transformation Determine which of

2. Let T Rm Rn be a linear transformation. Determine which of the following is FALSE. a. T (0) 0 b. T(cu dv 3 (a) dT(v) for all scalars c, d and u, v E Rm. c. If T(ar) Aar, then b is in the range of Tif and only if Az b is consistent d If m n, T(r) Ar, and every column of A is a pivot column, then the range of Tis R\" e. none of these

Solution

a) True because for every Null input there will be trivial solution

b) True: because transformation is linear cmbination of u and v

c) False

d) True: because A will contain all the vectors including b, in its column space