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Determine which values of k will give, one Solution, no Solution, or infinitely Many Solutions
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- čas přidán 5. 09. 2020
- ❖ In this problem, we determine values of unknown constant k, if any, will give one solution (a unique solution), no solution infinitely, many solutions to the system of equations.
This video presents linear algebra in the School of Mathematics and Statistics which is in the Faculty of Science in most universities.
The link to this playlist (Linear Algebra):
• Linear Algebra
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Thank you so much.... You don't know how helpful this video is.... Highly recommend to friend circle.. Already shared and subscribed!!!
Glad it helped! thanks, and good luck 😇
absolute life saver! i have a test in linear algebra after 2 days and this made me understand the concept easily and in a clear way.
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thank you for explaining it. you don't know how much help you have done
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If you have any more questions, please don't hesitate to let me know. Thanks for watching and for your kind words 😇
You are a real one for making this man! Thank you so much!
I appreciate that & you are most welcome
It's great seeing young Arabs entering the English side of educational CZcams videos.
Thank you very much. You explained it very well and clearly, so it helps me to understand it very well. Thank you again.
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Thanks sir...for discussing such example..it cleared remained doubts
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Actually understood the concept. Thanks!
Great! & Thanks for watching 😇
Thank you so much. Greatly appreciate this video
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Man thank you so much, you've explained it so well💪💪
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Wherever you’re man God bless you....This is a great video...
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Really good explanation!Hoping for more videos
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😊
Thank you 😊 I'm writing on this concept this afternoon
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Thank you! Well explained!
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thank you very much....this was very helpful
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in just 13 mini l have understood the topic thank you
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I know this is a kind of old video, but just want to say this really helped me. You're a great teacher. Liked and subscribed.
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Thanks a lot sir❤
Most welcome 😇
hi sir, your playlist in linear algebra is the BEST in youtube , but i just want to ask about step in this video 5:23 I think we should also do the R1-2R2 too to make the 2 above the leading 1 in the second column 0 too right?
Glad to hear that 😇
We only care about the value of k in the last row, so you don't have to do it because it will not affect the answer.
Also, you can't make the above (k^2)-4 zeros (can't make the rest of the third column zeros) unless k is given.
Great video!
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Thanku ❤️
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great problem and solution!
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Thanks for overcome my pressure
Any time & glad to heart that!
thank you so much ❤
You're welcome & thank for watching 😊
Thanks alot.
Most welcome!
What do you do if the k variable is in the 1st column instead of the 3rd?
Usually, the variable k is placed in the 3rd row. However, placing k in the 1st column doesn't change the solution set. This is similar to how the equation x+y+z=1 is equivalent to z+y+x=1.
To illustrate this, let's take the linear system:
x + 2y + z = 1
x + 3y + 2z = 1
((k^2)-9)x - 5y - 4z = k + 1.
You can rearrange this system by swapping the 1st and 3rd columns, which leads to another system of equations with the same solutions. Note that in this rearranged system, the solution vector would be x=[z;y;x] instead of x=[x,y,z]:
z + 2y - x = 1
2z + 3y + x = 1
-4z - 5y + ((k^2)-9)x = k + 1.
This gives the same solutions as discussed in this video.
If you have further questions or would like additional illustrations, don't hesitate to ask & Good luck!
Thank you
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Amazing 🤩🤩
Thanks 🤗
thank you
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finally understood this, thank you
I'm so glad to hear you've finally understood it! You're very welcome. Keep up the good work, and if you have any more questions, just let me know 😇
Thanks
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If there were no k's in the 3x1 right hand matrix, and so you end up with k + or - some constant in the left hand matrix in the reduced echelon form is just equal to another non-zero constant, does that mean it can only have infinitely many solutions or no solutions, and there is no way it could have a unique solution?
If there is no k on the right-hand side ( it means that the last row will be [-4 -5 (k^2)-9 | 1] ), then
there is no way to have infinitely many solutions since you cannot make a zero row for any value of k ( e.g. [0 0 0|0] ).
My brother you are the man!!... Thanks you so much for the video brother. A similar problem to that one has been giving me a headache since morning. Thanks man !
Thank you so much for your kind words! I'm really glad the video was able to help you out with that problem 😇
If you have any more questions or need further explanations, feel free to ask. Thanks for watching, and keep up the great work 👍
May I ask if the K is in column 2, can I just swap the entire column 2 with column 3?
Thanks alot !
When you start solving a problem using the Reduced Row Echolen Form (RREF), you cannot swap columns. As you can see from the name of the form, the Reduced 'Row' Echolen Form is designed to work only between rows.
As an example, consider the following equations:
x - z + 2y = 1
2x + z + 3y = 1
-4x + ((k^2)-9)z - 5y = k + 1
You can then rearrange the equations as follows:
x + 2y - z = 1
2x + 3y + z = 1
-4x - 5y + ((k^2)-9)z = k + 1
All we have changed is how we have arranged them from the beginning, then the steps will still be the same.
In the end, you just care about k values.
@@Mulkek this comment literally made me pass linear algebra thank you!!
its supposed to be k^2 - 8 not "-4" but thanks for the explanation
Could you explain more about what did you mean by k^2 - 8 not "-4" (e.g. you can tell the time)? & thanks for watching 🙂
sir can you help me with a certain question
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!
Don Deezy
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