Vector Space and Subspace Help

Hi everyone,

I am trying to learn linear algebra using Brilliant and Khan Academy. For some reason I can't grasp vector spaces and subspaces using both of these platforms. The explanations are just incredibly convoluted to me. I am getting extremely lost on the following two quizzes in Brilliant: and

At this point I'm thinking of just moving to a textbook to learn the rest of linear algebra. Any help is appreciated and if anyone know of a good linear algebra book that teaches these concepts well then please let me know.

Note by Brandon Quintero
9 months ago

No vote yet
1 vote

  Easy Math Editor

This discussion board is a place to discuss our Daily Challenges and the math and science related to those challenges. Explanations are more than just a solution — they should explain the steps and thinking strategies that you used to obtain the solution. Comments should further the discussion of math and science.

When posting on Brilliant:

  • Use the emojis to react to an explanation, whether you're congratulating a job well done , or just really confused .
  • Ask specific questions about the challenge or the steps in somebody's explanation. Well-posed questions can add a lot to the discussion, but posting "I don't understand!" doesn't help anyone.
  • Try to contribute something new to the discussion, whether it is an extension, generalization or other idea related to the challenge.
  • Stay on topic — we're all here to learn more about math and science, not to hear about your favorite get-rich-quick scheme or current world events.

MarkdownAppears as
*italics* or _italics_ italics
**bold** or __bold__ bold

- bulleted
- list

  • bulleted
  • list

1. numbered
2. list

  1. numbered
  2. list
Note: you must add a full line of space before and after lists for them to show up correctly
paragraph 1

paragraph 2

paragraph 1

paragraph 2

[example link]( link
> This is a quote
This is a quote
    # I indented these lines
    # 4 spaces, and now they show
    # up as a code block.

    print "hello world"
# I indented these lines
# 4 spaces, and now they show
# up as a code block.

print "hello world"
MathAppears as
Remember to wrap math in \( ... \) or \[ ... \] to ensure proper formatting.
2 \times 3 2×3 2 \times 3
2^{34} 234 2^{34}
a_{i-1} ai1 a_{i-1}
\frac{2}{3} 23 \frac{2}{3}
\sqrt{2} 2 \sqrt{2}
\sum_{i=1}^3 i=13 \sum_{i=1}^3
\sin \theta sinθ \sin \theta
\boxed{123} 123 \boxed{123}


Sort by:

Top Newest

Hello Sir, I am not a premium member, but as far as I know, Brilliant courses are really easy to friend is learning about Artificial Neural Networks from this site only......But, well I am more of a bookreader, and I have learnt Linear Algebra from this.........I hope it helps...:) Also, my uncle had suggested me to read, maybe this can help too...:)

Aaghaz Mahajan - 9 months ago

Log in to reply

Thank you for the recommendations! I usually don't have an issue understanding explanations given on Brilliant and Khan Academy but for some reason Linear Algebra is giving me more trouble than I've experienced before. I found a Linear Algebra series on Youtube by the creator 3blue1brown and his explanations has helped me a lot so far.

Brandon Quintero - 8 months, 4 weeks ago

Log in to reply

My pleasure!!! And yes, 3blue1brown makes AMAZING videos.....!! Did you see his video regarding relation between number of elastic collisions and the digits of pi??

Aaghaz Mahajan - 8 months, 4 weeks ago

Log in to reply


Problem Loading...

Note Loading...

Set Loading...