MATH1131 Linear Algebra: Chapter 4 Problem 17

In this problem we determine values of unknown constant k, if any, will give unique solution, no solution infinitely many solutions to the system of equations. Presented by N J Wildberger of the School of Mathematics and Statistics, Faculty of Science, UNSW.

[joaosousa]

this video literally saved me for my linear algebra test thanks from brazil

[kojuntan]

Thanks the explanation was very clear and precise!

[clintonnavicha]

Thank you very much just gained me 10+ marks in my exam tomorrow

[apnihorrorduniya]

Amazing sir ❤️ happy teacher's day

[igbadumhejesse]

I had a test today and it was this same question. thank you

[cormacredmond]

great explanation helped a lot thanks very much!

[randysalimsma]

thankyou so much sir, you help my final examination preperation

[denisgodwin]

thanks so much sir, dervis from Tanzania

[lucaleone]

Thank you from Delft, the Netherlands!

[Mulkek]

Thanks, and it's so easy & simple!

[Xsjr]

I don't get it, our teacher told us that the system is solvable if the rank of the coefficient matrix equals the rank of the extended matrix. In this case, wether you put k = 3 or k # 3 doesn't make a difference since in both instances, the ranks of the two matrices are equal, therefore you should have a solvable system in either case.
And then she told us if the number of variables (x, y, z here) is equal to the rank of the coefficient matrix, then you have a unique solution. If the variables are more than the rank, then you have infinite solutions.
So here, if k = 3 it should mean we have infinite solutions, and when k # 3 then we have a unique solution.

Where am i going wrong?

[evelyntran]

thank you from winnipeg, manitoba <3

[shubhamdubey]

U r the best teacher till I heard many thank u sir

[eliekhoury]

what if you took if k=0 wouldn't that give you -3=3? so we will get the no solution option

[jaybarham]

Omg you sound like Christoph Waltz. It makes it so easy to listen

[maahasgharali]

How do you know till how long you have to keep on reducing the matrix. Like when u said at 4.49 "we are in a position to figure out..." how do you know. thanks in advance :)

[anirudhsingh]

We are studing this in our class 12th in india when you guys are teaching this in university