Answered

Explore Westonci.ca, the leading Q&A site where experts provide accurate and helpful answers to all your questions. Get quick and reliable solutions to your questions from knowledgeable professionals on our comprehensive Q&A platform. Join our Q&A platform to connect with experts dedicated to providing accurate answers to your questions in various fields.

Suppose Ax = b always has at least one solution no matter what b is. Why AT y = 0 has only the trivial solution y = 0?

Sagot :

facundo3141592

Answer:

For the first equation we have:

A*x = b

solving for x, we get:

x = b/A

If it always has a solution, then we can not have A = 0, because that causes an undefined operation.

so for example, if we have A = 1 and b = 2

x = b/A = 2/1

For the other case,

A*y = 0

dividing both sides by A

y = 0/A = 0

y = 0

Here we have only one possible solution, the trivial one, y = 0.

And the dependence on A disappears (because the quotient between zero and a number different than zero is always zero)

We hope you found what you were looking for. Feel free to revisit us for more answers and updated information. Thank you for your visit. We're dedicated to helping you find the information you need, whenever you need it. Thank you for visiting Westonci.ca. Stay informed by coming back for more detailed answers.