Відео

If the second and third rows are all 0s, yes, it usually means there are infinitely many solutions. This happens because there aren’t enough equations to find all the variables (x_2 and x_3).

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You're absolutely right! It's not necessary to perform R_1-2R_2 ---> R_1 if you observe that applying R_3 + 2R_2 -> R_3 leads to [0 0 0 0|1] ], which indicates no solution. Great observation! 👍

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Thank you so much! I’m glad you found the explanation easy to follow. Hopefully, more people will find it helpful over time! 😇

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For this problem, you can use row echelon form to determine the type of solution. Reduced row echelon form is also an option, but it’s not necessary unless you want further simplification. Good luck, and feel free to ask if you have any more questions 👍

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Thank you for your comment! Just to clarify, did you mean k^2−4 instead of a^2-5? Let me know, and I'd be happy to help 😇

You're very welcome! I’m glad the video was helpful. If you’re interested in more practice, feel free to check out my other video on a similar topic: "Find the values of k which give one Solution, no Solution, or infinitely Many Solutions", and here is the video link: ua-cam.com/video/61vt1nDHOKo/v-deo.htmlsi=3Dt2q1Q91RAzlJeq I'm planning to create more videos like this in the future, so stay tuned! 😇

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Thank you so much & I’m so glad you found the video Greatest of All Time 😇

Thank you so much! I’m really glad you found the video helpful 😇

You're so welcome & I’m really glad you found the video helpful 😇

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Thank you so much for your encouraging words! I’m thrilled to hear you enjoyed the content. Your support is incredibly valuable to me 😇

@@Mulkek you are welcome, I look forward to watching your upcoming videos, I can't wait 😄😂😄

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I’m so glad you found the video enriching. Your support inspires me to continue creating content that makes a difference. Thank you so much for your kind words & for following 😇

Thank you for your suggestion! I will definitely make a video on the Geometric Explanation and Derivation of a² - b² = (a+b)(a-b) very soon. It will be the next upload, so hit SUBSCRIBE to catch it first! Stay tuned 😇

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Thank you so much & I'm thrilled to hear that you found the video awesome and helpful 😇

Glad to hear you found it simple & Thanks for watching 😇

Thanks for your question! This video covers topics from Linear Algebra that are typically taught at the College or University Level, so it's more Advanced than GCSE. However, in some countries, the introduction to matrices, including operations like Addition, Subtraction, Multiplication, and Solving Systems like Two Equations with Two Variables, is part of the High School Mathematics Curriculum. If you're looking to understand the basics of Matrix Operations, you might find my other videos in the *Linear Algebra playlist* helpful. These include *Scalar Multiplication of Matrices* ua-cam.com/video/SK1jBwFh4t4/v-deo.htmlsi=Cf2mOTFBGfjMCldD *Adding and Subtracting Matrices* ua-cam.com/video/4WS9xCU07C0/v-deo.htmlsi=HTVnlWn15xefi66X *Multiplying Matrices* ua-cam.com/video/-_1QKxx_sus/v-deo.htmlsi=CrVenkYrVb1aob0i *Solving Two Linear Systems Using the Inverse* ua-cam.com/video/ZOFOx3g8Oq0/v-deo.htmlsi=DsoG0HgBsqfgELaA *Linear Algebra Playlist* ua-cam.com/play/PLPm9fyDNbwj9zUIHKYfNwkfeWWBamk-q_.html These topics might provide a good foundation and are definitely worth checking out if you're interested in Foundational Mathematics. Let me know if you have any other questions 😇

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Wow, that’s fantastic to hear😇! I’m so glad the video helped clarify things for you. It’s amazing what we can sometimes accomplish in just a short time with the right approach. Keep up the great work, and if you have any more questions as you continue to explore mathematics, feel free to ask. Thanks for watching and sharing your success with me! 😊

Your video are wonderful

Thank you so much for your kind words! I'm glad you found the explanation helpful. Stay tuned, more videos are on the way soon😊

You're absolutely right, calculating the inverse of a 4x4 matrix by hand can be quite time-consuming and complex, which is why it's often not covered at A-level without the aid of technology. It's great for deepening your understanding of matrix operations, though! If you ever decide to tackle it, patience and practice are key. Thanks for watching and sharing your thoughts 😇

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Welcome back! I'm glad to hear that you find the video helpful for your new course as well. It’s always good to revisit and reinforce these concepts. Best of luck with your studies, and if you have any questions, feel free to ask & thanks for watching again 😇

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You're welcome! I'm glad you found the video helpful. Thanks for watching & for your kind words! 😊

If you do R2 = R2 + R1 for matrix A, the second row will become [4, 6], which is not equal to the second row in matrix B: [5, 8]. So, this way is not sufficient to show that matrices A and B are row equivalent. Let me know if you have any more questions or need further clarification; feel free to ask & good luck with your studies 😇

Thank you so much! I’m really glad you enjoyed the video. Your support means a lot! 😇

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Thank you for the great feedback! I'm thrilled you enjoyed the video and appreciate your suggestion for a trigonometry video. It’s a fantastic idea, and I'm definitely considering creating a similar summary for trigonometry concepts. Stay tuned, and good luck with your studies! 😇

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Thanks for being the first to comment! Really appreciate it 😇

Of course, I'd be happy to help! Please share your question here, and I'll do my best to provide a clear explanation. Additionally, I'll consider addressing these types of questions in more detail in future videos. Looking forward to assisting you!