Let A be an 3 x 20 matrix with 3 pivots. a. Does Ax = 0 have a nontrivial solution? Defend your response. Your work should be legible, and all your logic should be clear and justified. Edit Insert Formats ▾ B I U x₂x² A A 글 블로 M <> Σ+ Σ Α E b. Does A = have at least one solution for each b & R³? Defend your response. Your work should be legible, and all your logic should be clear and justified.
Let A be an 3 x 20 matrix with 3 pivots. a. Does Ax = 0 have a nontrivial solution? Defend your response. Your work should be legible, and all your logic should be clear and justified. Edit Insert Formats ▾ B I U x₂x² A A 글 블로 M <> Σ+ Σ Α E b. Does A = have at least one solution for each b & R³? Defend your response. Your work should be legible, and all your logic should be clear and justified.
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:Let A be an 3 × 20 matrix with 3 pivots.
a. Does Ax = 0 have a nontrivial solution? Defend your response. Your work should be legible,
and all your logic should be clear and justified.
Edit
= = =
Insert Formats
▼
U
BIU
x₂ x² A A
دی 0 = =
Σ+ Σ Α
b. Does Ax =
have at least one solution for each & R³? Defend your response. Your work
should be legible, and all your logic should be clear and justified.
Expert Solution
Step 1
a. If A is 3*20 matrix then in equation form we have 3 equation and 20 unknown. Given that 3 pivot elements so we can say that 20-3=17 unknown are independent. If any unknown is independent then Ax=0 has a non trivial solution.
So, here 17 unknown are independent then this system have a non trivial solution.
So this is true.
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