Answered: If A is an nxn matrix, then the…

Advanced Engineering Mathematics

10th Edition

ISBN:9780470458365

Author:Erwin Kreyszig

Publisher:Erwin Kreyszig

Chapter2: Second-order Linear Odes

Section: Chapter Questions

Problem 1RQ

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For this exercise assume that the matrices are all

n×n.

The statement in 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. Mark the implication as False if "statement 2" is false but "statement 1" is true. Justify your answer.

For this exercise assume that the matrices are all n xn. The statement in 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. Mark the implication as False if
"statement 2" is false but "statement 1" is true. Justify your answer.
If A is an nxn matrix, then the equation Ax = b has at least one solution for each b in R".
Choose the correct answer below.
A. The statement is false. By the Invertible Matrix Theorem, Ax = b has at least one solution for each þ in Rh only if a matrix is invertible
B.
The statement is true. By the Invertible Matrix Theorem, if Ax = b has at least one solution for each b in R", then the matrix is not invertible.
C. The statement is false. By the Invertible Matrix Theorem, if Ax = b has at least one solution for each b in R", then the equation Ax = b has no
solution.
O D. The statement is true. By the Invertible Matrix Theorem, Ax = b has at least one solution for each b in R" for all matrices of size nxn.

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