Consider the system of equations ax +9y = 3 x + ay = 1. or what value(s) of the scalar a (if any) does the system have no solutions, nique solution or infinitely many solutions? For each such a, write down th orresponding solutions

Consider the system of equations ax +9y = 3 x + ay = 1. or what value(s) of the scalar a (if any) does the system have no solutions, nique solution or infinitely many solutions? For each such a, write down th orresponding 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'm currently struggling to solve this problem, and I was wondering if you could lend me a hand. The problem requires a solution using matrix form exclusively, with no other methods allowed. Could you kindly walk me through the solution step by step using matrix form until we arrive at the final answer?

I have provided both the question and the answer, but now I require a comprehensive, step-by-step explanation to guide me towards reaching that answer.

2.9. Consider the system of equations
ax +9y = 3
x + ay = 1.
For what value(s) of the scalar a (if any) does the system have no solutions, a
unique solution or infinitely many solutions? For each such a, write down the
corresponding solutions.

2.9 a = -3, no solutions. a = 3, infinitely many solutions
X
[3] =
y
a #3, a # -3, unique solution
=
1 3
3+a 1
x
+

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