Linear algebra-rank

Question

Questions:

Let A = | a₁₁    a₁₂    a₁₃ | Show that A has rank 2 if and only if one or more of the determinants
            | a₂₁     a₂₂   a₂₃ |

            | a₁₁   a₁₂ |  | a₁₁   a₁₃ |    | a₁₂      a₁₃ |   are non zero
            | a₂₁   a₂₂ |  | a21   a₂₃ |    | a₂₂      a₂₃ |

2. Use the result in Exercise 10 to show that the set of points (x, y, z) in R3 for which the matrix  | x y z |
                                                                                                                                                         | 1 x y |

has rank 1 is the curve with parametric equations x = t, y = t², z = t³

3. Prove: If k does not equal to zero, then kA have the same rank.