# Solution or explanation true since is not a solution

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n × n b 0 R n , A x = True. Since A 0 = 0 b , 0 is a solution to A x = b , and hence the set of solutions is not a subspace. b
Solution or Explanation True. Since is not a solution to and hence the set of solutions is not a subspace. False. Since A 0 = 0 b , 0 is a solution to A x = b , and hence the set of solutions is a subspace. b ,
17. 1/1 points | Previous Answers HoltLinAlg1 4.1.046. Determine if the statement is true or false, and justify your answer. If A is a matrix, then null( A ) forms a subspace of 6 × 4 R 6 True, by the theorem that says if A is an n × m matrix, then the set of solutions to the homogeneous linear system A x = 0 forms a subspace of R False. For any 6 × 4 matrix A , null( A ) is a subspace of R . n . 4 . .
Solution or Explanation False. For any matrix A , null( A ) is a subspace of not False. For any 6 × 4 matrix A , null( A ) is a subspace of R 2 . R . .
18. 1/1 points | Previous Answers HoltLinAlg1 4.1.048. Determine if the statement is true or false, and justify your answer. Let be a linear transformation. Then is a subspace of . . . . . .
Solution or Explanation True, by Theorem 4.5 that says let T : R m R n be a linear transformation. Then the kernel of T subspace of the domain R m is a .
19. 1/1 points | Previous Answers HoltLinAlg1 4.1.050. Determine if the statement is true or false, and justify your answer. Let be a linear transformation. Then is a subspace of Solution or Explanation False, because is a subspace of the codomain not the domain T : R 2 R 8 range( T ) R 2 True, by the theorem that says let T : R m R n be a linear transformation. Then the range of is a subspace of R m False, because range( T ) is a subspace of R 8 . T . . . . .