Mathematics, 22.05.2020 22:03 SmolBeanPotato
For this exercise assume that the matrices are all ntimesn. Each part of this exercise is an implication of the form "If "statement 1", then "statement 2"." Mark an implication as True if the truth of "statement 2" always follows whenever "statement 1" happens to be true. An implication is False if there is an instance in which "statement 2" is false but "statement 1" is true. Complete parts a through e. Justify each answer.
If the equation Ax= 0 has only the trivial solution, then A is row equivalent to the n×n identity matrix
A. False; by the Invertible Matrix Theorem if the equation Ax 0 has only the trivial solution, then the matrix is not invertible. Thus, A must cannot be row equivalent to the n x n identity matrix.
B. True: by the Invertible Matrix Theorem if equation Ax= 0 has only the trivial solution, then the equation matrix is not invertible. Thus, A cannot be row equivalent to the nxn identity matrix. Ax - b has no solutions for each b in R". Thus, A must also be row equivalent to the n x n identity matrix
C. True; by the Invertible Matrix Theorem if the equation Ax=0 has only the trivial solution, then the matrix is invertible. Thus, A must also be row equivalent to the n x n identity matrix.
D. False; by the Invertible Matrix Theorem if the equation Ax 0 has only the trivial solution, then the matrix is not invertible; this means the columns of A do not span R". Thus, A must also be row equivalent to the nx n identity matrix
Answers: 1
Mathematics, 21.06.2019 16:00
Find the greatest common factor of the polynomial: 10x^5+15x^4-25x^3 10x^5 x^3 5x^3 5
Answers: 2
Mathematics, 21.06.2019 17:00
Select all of the quadrants that the parabola whose equation is y=√x-4 (principal square root) occupies. i ii iii iv
Answers: 3
Mathematics, 21.06.2019 20:00
Given: ∆mop p∆mop =12+4 3 m∠p = 90°, m∠m = 60° find: mp, mo
Answers: 1
For this exercise assume that the matrices are all ntimesn. Each part of this exercise is an implica...
Mathematics, 17.02.2022 01:00
Mathematics, 17.02.2022 01:00
Biology, 17.02.2022 01:00
Social Studies, 17.02.2022 01:10
SAT, 17.02.2022 01:10
Biology, 17.02.2022 01:10
History, 17.02.2022 01:10
English, 17.02.2022 01:10
Biology, 17.02.2022 01:10
History, 17.02.2022 01:10