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15. 2/2 points | Previous Answers HoltLinAlg1 4.1.036. Let for the matrix A . Determine if the vector b is in the kernel of T . Determine if the vector c is in the range of T . T ( x ) = A x A = , b = , c = 1 2 3 4 5 6 7 8 9 1 −2 1 1 4 7 The vector b is in the kernel of T . The vector b is not in the kernel of T . The vector c is in the range of T . The vector c is not in the range of T .
±²³´²µ¶³· 8: &RPPRQ 0DWK ±¶¸ 6HFWLRQ ´¹³ 16. 1/1 points | Previous Answers HoltLinAlg1 4.1.045. Determine if the statement is true or false, and justify your answer. If A is an matrix and is in then the solutions to do not form a subspace. n × n b 0 R n , A x = b
±²³´²µ¶³· 8: &RPPRQ 0DWK ±¶¸ 6HFWLRQ ´¹³ 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 Solution or Explanation False. For any matrix A , null( A ) is a subspace of not 7 × 5 R 7 . 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 n .
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 is a subspace of the domain R m .