## Question

###### 4. (10 points) Let A be an m X n matrix with rank(A) =r. If P and m X m and n X n matrices, respectively:are invertible(a) Prove that rank(PA) =T by proving that PA and A have the same nullspaceProve that rank( AQ) by proving that AQ &nd A have the same nullspace. Hint: Recall that rankA = rankAT

4. (10 points) Let A be an m X n matrix with rank(A) =r. If P and m X m and n X n matrices, respectively: are invertible (a) Prove that rank(PA) =T by proving that PA and A have the same nullspace Prove that rank( AQ) by proving that AQ &nd A have the same nullspace. Hint: Recall that rankA = rankAT

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