Consider 3 times 2 matrices A Decide whether the following s

Consider 3 times 2 matrices A. Decide whether the following statements must be true for all A, for some A or of no A. im(A) = R^3 ker (A) = {0^rightarrow} im(A) contains two linearly independent vectors v^rightarrow_1, v^rightarrow_2, R^3. ker (A) = span (v^rightarrow_1, v^rightarrow_2) for some v^rightarrow_1, v^rightarrow_2, R^2.

Solution

dim im(A) is max 2 only so option a is true for no A

b) ker (A) is not zero it is true for no A

option c is true for some A

it is for some A