For this exercise assume that the matrices are all nxn. 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 the linear transformation x → Ax maps R into R, then A has n pivot positions. Choose the correct answer below. A. The statement is false. According to the Invertible Matrix Theorem, x → Ax maps R B. The statement is true. The linear transformation x → Ax will always map R into R the Invertible Matrix Theorem, A has n pivot positions. OC. The statement is false. The linear transformation x → Ax will always map R into R Invertible Matrix Theorem, A has n pivot positions only if x → Ax maps R onto R. into R, then A has n +2 pivot positions. for any nxn matrix. Therefore, according to for any nxn matrix. According to the O D. The statement is true. According to the Invertible Matrix Theorem, if x → Ax maps R into R then A is invertible, and if a matrix is invertible it has n pivot positions.
For this exercise assume that the matrices are all nxn. 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 the linear transformation x → Ax maps R into R, then A has n pivot positions. Choose the correct answer below. A. The statement is false. According to the Invertible Matrix Theorem, x → Ax maps R B. The statement is true. The linear transformation x → Ax will always map R into R the Invertible Matrix Theorem, A has n pivot positions. OC. The statement is false. The linear transformation x → Ax will always map R into R Invertible Matrix Theorem, A has n pivot positions only if x → Ax maps R onto R. into R, then A has n +2 pivot positions. for any nxn matrix. Therefore, according to for any nxn matrix. According to the O D. The statement is true. According to the Invertible Matrix Theorem, if x → Ax maps R into R then A is invertible, and if a matrix is invertible it has n pivot positions.
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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Transcribed Image Text:For this exercise assume that the matrices are all nxn. 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 the linear transformation x → Ax maps R into R", then A has n pivot positions.
Choose the correct answer below.
OA. The statement is false. According to the Invertible Matrix Theorem, x → Ax maps R
B. The statement is true. The linear transformation x → Ax will always map R into R
the Invertible Matrix Theorem, A has n pivot positions.
O C. The statement is false. The linear transformation x → Ax will always map R into R
Invertible Matrix Theorem, A has n pivot positions only if x → Ax maps R" onto R".
into R", then A has n +2 pivot positions.
for any nxn matrix. Therefore, according to
for any nxn matrix. According to the
O D. The statement is true. According to the Invertible Matrix Theorem, if x → Ax maps R" into R then A is invertible, and if a matrix is
invertible it has n pivot positions.
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