[Linear Algebra] Matrix-Vector Equation Ax=b

We learn how to solve the matrix equation Ax=b.

#LinearAlgebra #Algebra #UniversityMath #Lecture

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We discuss the matrix-vector equation Ax=b.

Hello, welcome to TheTrevTutor. I'm here to help you learn your college courses in an easy, efficient manner. If you like what you see, feel free to subscribe and follow me for updates. If you have any questions, leave them below. I try to answer as many questions as possible. If something isn't quite clear or needs more explanation, I can easily make additional videos to satisfy your need for knowledge and understanding.

[rajatsethi]

If anyone wishes to understand Linear Algebra go and watch Essence of Linear Algebra and then come back here to see how problems are solved. Things become very clear after this.

[hero_of_winds]

Thanks so much! My teacher did a good job of explaining this, but I couldn't quite wrap my head around it like other students did. Having it explained in a different way helped!

[Assault_Butter_Knife]

Alright, but what if the matrix is the unknown element? I am currently studying symmetries and I often get cases like C(1, 2, 3)=(2, 1, 3) where C is some operation. How would I find the matrix C which facilitates this transformation?

[juniorcyans]

I knew how to do dot product and I did a lot of complicated matrices in my mathematical physics class, but I didn’t know why until now!

[AP-pmqy]

At 6:03 I did it the other way round. Is it still correct?

[rosskious]

n lives in m is the reason that you might have a vector with 6 places and end up with 4 or however many rows you have in your matrix.

[omkx]

Thank u very much, really i found it helpful💛.

[jayyo]

Probably just a weird graphical coincidence - but is there anything to the analogy that the coloumns and rows being orthogonal directions, produce the same as the n (dot) x = n (dot) p rule for deriving general equations from the norm and direction-to-point vectors?

[Voyd]

Hold up now I'm in grade 9, this isn't what we're learning, I'm not ready for this yet, wrong video.

[chienphung]

why didn''t you reduce to pivot position in the last example

[rakshityadav]

This is a MCQ type question Tick the correct answer...:-

for the given set of simultaneous equations
1.5x -0.5y =2
4x+2y+3z=10
7x+y+5z=10
choose correct one of the following:-
1) solution is unique
2) infinitely many solution exist
3) Equation are incompatible
4) finite number of multiple solution exist.

please answer this and explaination also. i.e. PLEASE SOLVE .

[chaz_eptv]

Why didn’t you reduce the last matrix to REF?

[MasayoMusic]

In the last example. That is the only solution right? There is only one unique solution? Thank you.

[maxpercer]

Strictly speaking

[ *a1* ... *an* ] . [ x1]
[ x2 ]
.
.
.
[xn]

is a slight abuse of notation using a dot product.
Dot products are used to take product of two lists (not specifically using matrices).
But this still works as a heuristic, it is valid.
In general a dot product operates on two lists of numbers.

[ratyrat]

it seems so far that linear algebra is just having different funny ways to say "put into augmented matrix, convert to RREF, solve"

[bintkay]

How did u deduce the final results from the matrix? I.e 2x =6

[okianderson]

stuck at 8:37. why did you not reduce to REF