(iv) (x+2y = 0 (ax+day=0 aER (Ab) = (1 2²10)₁₁ (63) If a to, then (A) = or(Alb) = 2 and there exists no solution It a=o, then r(A) = 1 = r(Alb) and there exists infinitely many We solve x+2y = a and the solution set is: R₂-apı va-at { (₂) = (²+ ²² ) : + ER } solutions
(iv) (x+2y = 0 (ax+day=0 aER (Ab) = (1 2²10)₁₁ (63) If a to, then (A) = or(Alb) = 2 and there exists no solution It a=o, then r(A) = 1 = r(Alb) and there exists infinitely many We solve x+2y = a and the solution set is: R₂-apı va-at { (₂) = (²+ ²² ) : + ER } solutions
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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Question
I have uploaded the question and the answer the answer is correct I got it from the solution sheet the part I don’t understand is included in the red bracket
I don’t understand where the conditions if =0 and not =0 occur how can I know r(A)=1 or 0 or 2 like those stuff and same thing for r(A|b) I don’t know where these numbers come from if you can show me please with an example.
Transcribed Image Text:(iv) √x+2y=0 aER
[ax+day=0
(A/B) = (1 ₂²1 0) ₁-RE-OR₁ (0 |
If a 0, then (A) = or(Alb) = 2 and there exists no solution
It a=o, then r(A) = 1 = r(Alb) and there exists infinitely many
We solve x+2y = a and the solution set is:
va-at
{(₂) = (*+ **): + ER}
t
solutions
Transcribed Image Text:Exercise4.3. For all a E R decide whether the following linear systems have solutions and
if solutions exists find all of them:
(i) {
{
(iv)
x + 2y = 0
ax + 3y = 0'
[ x + 2y = a
ax+ 2ay = 0
(ii)
{
x + 2y = 0
ax+ 2ay = 0
(iii)
x + 2y = a
ax+3y=0"
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