Learning starts with a question. Asking is a signal for knowledge request!
First time here? Checkout the FAQs!

*Math Image Search only works best with SINGLE, zoomed in, well cropped images of math. No selfies and diagrams please :)

0 like 0 dislike
Let \(A: \mathbb{R}^{n} \rightarrow \mathbb{R}^{k}\) be a real matrix, not necessarily square.

a) If two rows of \(A\) are the same, show that \(A\) is not onto by finding a vector \(y=\) \(\left(y_{1}, \ldots, y_{k}\right)\) that is not in the image of \(A\). [HINT: This is a mental computation if you write out the equations \(A x=y\) explicitly.]
b) What if \(A: \mathbb{C}^{n} \rightarrow \mathbb{C}^{k}\) is a complex matrix?
c) More generally, if the rows of \(A\) are linearly dependent, show that it is not onto.
in Mathematics by Platinum (101k points) | 275 views

Related questions

0 like 0 dislike
0 answers
asked Jan 21, 2022 in Mathematics by MathsGee Platinum (101k points) | 390 views
0 like 0 dislike
0 answers

Join MathsGee Q&A, where you get instant answers to your questions from our AI, AstraNova and verified by human experts. We use a combination of generative AI and human experts to provide you the best solutions to your problems.

On the MathsGee Q&A, you can:

1. Get instant answer to your questions

2. Convert image to latex

3. AI-generated answers and insights

4. Get expert-verified answers

5. Vote on questions and answers

6. Tip your favorite community members

7. Join expert live video sessions (Paid/Free)

8. Earn points by participating

9. Take a course

10. Enjoy our interactive learning resources

Posting on the MathsGee Q&A

1. Remember the human

2. Act like you would in real life

3. Find original source of content

4. Check for duplicates before publishing

5. Read the community guidelines

MathsGee Q&A Rules

1. Answers to questions will be posted immediately after moderation

2. Questions will be queued for posting immediately after moderation

3. Depending on the number of messages we receive, you could wait up to 24 hours for your message to appear. But be patient as posts will appear after passing our moderation.

MathsGee Q&A


Social Proof

Web Analytics