Let A be an
matrix, and B an
matrix. Then the null space of B is a subspace of the null space of AB.

Name: Let A be an matrix, and B an matrix. Then the null space of B is a subspace of the null space of AB.
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Question

Let A be an 
  matrix, and B an 
  matrix. Then the null space of B is a subspace of the null space of AB.

Quizplus · Accepted Answer

Let x be in the null space of B, then Bx = 0. Multiplying both sides by A, we get A(Bx) = 0. But A(Bx) = (AB)x, so we have (AB)x = 0. Thus, x is also in the null space of AB, showing that the null space of B is a subspace of the null space of AB.

Let a Be an