This is the best video I've come across for Matrices and Determinants. Been trying to figure out some speed tricks for almost a year now and I can't tell you how useful this is! Thank you!
The problem with determinants and inverses is that the algorithm is always taught without explanation of what you are doing. The determinant corresponds to "volume change" so (absolute value) det=1 is a rotation or reflection, det>1 is something getting bigger, det
So I teach 17/18 year olds about this process to find the inverse. I would say from my experience that it is often better to explain the process, make sure everyone can do it consistently and reliably and then at a later point return to it and explain why it works and all that. We often look back at stuff once we have discovered why something works and go oh I wish I had been told that when we did it but neglect the fact that for most learners that is just an overload! And they get so confused they don't know what is going on. I would say when I used to explain the why as part of teaching the how in the same lesson or in adjacent lessons then the bottom half of the class starts doing weird things. Understanding why you get the determinant from the matrix times it's inverse and particularly why you get the 0s is a lot for students when they first encounter this. Later in the course they are better equipped to then understand why. I am a massive advocate for teaching why, students should be taught to ask why and be told why things are true etc from the youngest age throughout schooling. But there is also a careful balance that I've come to appreciate more in sometimes delaying that why for a little bit to aid clarity. But agree most other teachers at this level would never explain why it works and I think that is a real shame!😢
Glad that i discovered your channel, now I can study math even I didn't understand what the teacher was teaching in the class, love your content, Jesus bless.
Another method to find the A inverse without using adjoint First we find the determinant Then we assume an equation that det ( A - xI ) = 0 , We try to solve the det which is easier after already finding det then we get an equation of x ( degree of equation= order of the matrix ) Now the given matrix satisfies the equation In the case of the matrix in the video , we get the equation as -x³ + 22x +12= 0 We can put the matrix A in place of x -A³ + 22A + 12I= 0 A³ - 22A - 12I = 0 We multiply the whole equation by A inverse A² - 22 I - 12 (A inverse ) = 0 Then we can find the A inverse Here I is identity Matrix
Anything times 0 is zero (-x)×0= 0 , let's say, xand y are positive numbers (-x)×(y-y)=0 (-x)(y)+(-x)(-y)=0 (-x)(-y)-xy =0 ( we know ,neg × pos = neg) Adding xy to both side of the equation, (-x)(-y)-xy+xy= xy (-x)(-y)= xy So , neg × neg = pos
I was not expecting linear algebra to be considered math basics! This is rather advanced stuff, in my opinion
It's a part of high school curriculum 😊 Doesn't mean I'd remember this if I woke up at night 😂
Abhorred that class in college 😩😩😩
I studied this in 8th grade for a maths olympiad .
@@astroadhds9407 yeah I’ve seen matrix problems on standardized tests like the ACT before. Some are very basic in nature.
@@ThePowerfulOne07 they were teaching us this for mainly linear equations in 2 or 3 variables and for IOQM.
This is the best video I've come across for Matrices and Determinants. Been trying to figure out some speed tricks for almost a year now and I can't tell you how useful this is! Thank you!
Thanks!!
The "quick" way of computing determinant is also taught by my teacher, but I personally don't like to copy the columns as it looks messier.
Can you do an example for a 4x4 matrix
Awesome. Thanks again for your brilliance.
I wanted to know this! Thanks
The problem with determinants and inverses is that the algorithm is always taught without explanation of what you are doing.
The determinant corresponds to "volume change" so (absolute value) det=1 is a rotation or reflection, det>1 is something getting bigger, det
So I teach 17/18 year olds about this process to find the inverse. I would say from my experience that it is often better to explain the process, make sure everyone can do it consistently and reliably and then at a later point return to it and explain why it works and all that.
We often look back at stuff once we have discovered why something works and go oh I wish I had been told that when we did it but neglect the fact that for most learners that is just an overload! And they get so confused they don't know what is going on.
I would say when I used to explain the why as part of teaching the how in the same lesson or in adjacent lessons then the bottom half of the class starts doing weird things. Understanding why you get the determinant from the matrix times it's inverse and particularly why you get the 0s is a lot for students when they first encounter this. Later in the course they are better equipped to then understand why.
I am a massive advocate for teaching why, students should be taught to ask why and be told why things are true etc from the youngest age throughout schooling. But there is also a careful balance that I've come to appreciate more in sometimes delaying that why for a little bit to aid clarity.
But agree most other teachers at this level would never explain why it works and I think that is a real shame!😢
Is there any reason why we need copy the 2 columns? Like is it figure out by you or there’s a theory at the back
So easy understand for me thanks✨️🥰
Fantastic method!
Glad that i discovered your channel, now I can study math even I didn't understand what the teacher was teaching in the class, love your content, Jesus bless.
Works like a charm
Thank u
I think Dodgson condensation is an even easier/faster way to get the determinant
I think the normal way of finding it is best.it it is Difficult to memorize trick
This is called the lattice method, it is faster in the end. Really not much of a learning curve.
Another method to find the A inverse without using adjoint
First we find the determinant
Then we assume an equation that det ( A - xI ) = 0 ,
We try to solve the det which is easier after already finding det
then we get an equation of x ( degree of equation= order of the matrix )
Now the given matrix satisfies the equation
In the case of the matrix in the video , we get the equation as -x³ + 22x +12= 0
We can put the matrix A in place of x
-A³ + 22A + 12I= 0
A³ - 22A - 12I = 0
We multiply the whole equation by A inverse
A² - 22 I - 12 (A inverse ) = 0
Then we can find the A inverse
Here I is identity Matrix
Cofactor expansion is still fastest because of the fewer multiplications
god bless you.
Bro why do i think its more longer method. Original method is easy for me cuz i'm used to it. Would be very hard to adapt on this one
Fastest way? Ti-84 matrix stuff.
until they include algebraic terms like k in the matrix and ask u for the inverse in terms of k😢😢
@@AhmedAhmed-iv1ly If you look for k, then you can put it into the equation solver.
Or if you are doing a cross product and the first row is i,j,k unit vectors. No numbers.
@@stephenbeck7222 That requires too much actual knowledge.
I must of blocked out this topic in school, or my advanced math teacher wasn't s big fan of matrices
The fastest way is to use the MINV(...) and the MDETERM(...) functions in the MS_Excel
Try by other no
Sir plz make a video on how negative times negative become positive.plz sir
Anything times 0 is zero
(-x)×0= 0 , let's say, xand y are positive numbers
(-x)×(y-y)=0
(-x)(y)+(-x)(-y)=0
(-x)(-y)-xy =0 ( we know ,neg × pos = neg)
Adding xy to both side of the equation,
(-x)(-y)-xy+xy= xy
(-x)(-y)= xy
So , neg × neg = pos
It's not "quick". The number of calculations are the same.
No sane person does Matrices by hand
I still do. Doesn't take that long and keeps my mind sharp.
In exams , you have to do it by hand
Math students do them by hand most of the time
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Your English......catsttroph, improve