How to Find eigen value and eigen vector of a 3X3 matrix | AspHero

hello guys welcome to this video today we are going to solve engineering mathematics start problem or eigenvalue and eigenvector we have a given matrix 2 1 1 1 2 1 0 0 1 ok we will find begin value and you get vector of this matrix ok let us start we have given matrix equals to 2 1 1 1 2 1 0 0 1 ok we have given matrix of 3 by 3 matrix yes now we know we have a formula modulus of a minus lambda I goes to 0 this modulus sign is modulus against the determinant of a minus lambda I is equals to 0 now we have you determinant of a that is 2 1 1 1 2 1 0 0 1 which is given here this a yes same we write here and minus lambda into if we have given 2 by 2 matrix then we have to write I equals to 1 0 0 1 yes this is 3 by 3 matrix so 4 3 by 3 matrix I equals to 1 0 0 0 1 0 0 0 1 this will write hi ok ok 1 0 0 0 1 0 0 0 1 yes now I will close this and it's equals to 0 ok now we'll multiply this lambda with this it's and solve this - - - - - - - - - now you have to minus lambda for this and we remove this row and this column and remaining 2 minus lambda 1 0 1 minus lambda okay for this kind of finding determinant we have a system that is if you are starting then you take this Chomp and you will omit this column you will omit this column okay omit this column and no this column and this row and you take only this into here 2 minus lambda 1 0 1 minus lambda yes and in second istic will do same for one okay now in second we have two right - yes it's a rule okay per second only you have - right - and then similarly for one you have to remove order this column element and this row element yes and remaining are this this this means I will do it again to minus lambda 1 1 1 to minus lambda 1 0 1 minus lambda that's not similarly for 1 we have 1 1 0 1 minus lambda 1 1 0 and for sine of 1 now we have to write to us ok only for second term we have to write minus and again one for one not taking this column and not taking this row what we have remaining 1 2 minus lambda 0 0 again for this 1 2 minus lambda 0 0 now that is proceed now we multiply this to minus lambda 1 minus lambda minus 2 into 1 minus now this much for first time okay now - for second term 1 into 1 minus lambda minus 0 into 1 plus 1 1 into 0 minus 0 into 2 minus lambda goes to 0 we are just doing multiplication only for that you know how we do that multiplication is okay I will so multiplication for this line again but this time but we have in this line was 2 minus lambda and we have remaining 2 minus lambda 1 0 1 minus lambda hence for this what we do first we take 2 minus lambda and in bracket we write 2 minus lambda okay cross multiplication here multiply this into this okay 2 minus lambda into 1 minus lambda now - okay after multiplying this this term this time for storms will take - n again multiply this term with this term now 0 in one okay then we have done with this part well we have finished this part and here you are moving second town okay well there is - at first and similarly will multiply in this way okay in this will we have done our cross multiplication part determinant there are two kinds of cross multiply so one is for normal equation we do want Crossman squeeze and one for finding determinant okay moving we have to minus lambda bracket 21 to minus 2 into lambda to lambda minus lambda minus minus plus lambda square bracket screws and we have minus 1 and package 1 1 minus lambda yeah - 0 ok and again here 1 into 0 0 0 into 2 minus lambda 0 so we don't drive this Tom and equals to 0 yes minus lambda bracket here lambda square minus 3 lambda plus 2 minus 1 is 1 1 minus minus plus 1 is 2 lambda lambda goes to 0 again I didn't quit multiply this term now 2 into lambda square 2 lambda square minus 2 3.6 lambda 2 into 2 that is 4 now minus lambda into lambda square lambda cube minus minus plus lambda into 3 lambda 3 lambda square minus plus plus minus plus minus and lambda into 2 2 lambda and we have here minus 1 plus lambda goes to 0 or have 4 we will write from this constant okay and minus this you can write directly for constant 4 minus 1 that is 4 minus 1 3 yes and now we will go for only single lambda minus 6 lambda minus 2 lambda that is minus 8 lambda plus lambda means minus 7 lambda minus lambda and now we will go for a square yeah 2 lambda square plus 3 lambda square that is 5 lambda square plus 5 lambda square here we have 5 lambda square and again we go for lambda cube 4 lambda cube we have only one term that is minus lambda Q yes it goes to 0 now we can write this is lambda q when we multiply both sides with - we can write in this form also lambda cube this plus will this minus will be plus and similarly this plus will be minus 5 lambda square and this minus will be plus 7 lambda and this Plus will be minus that is 3 goes to 0 time the cube minus 5 lambda square plus M lambda minus 3 equals 2 you know now you can solve it that tetration method also or you can directly use your calculator to find the solution of lambda okay in some cases it's easy to find in from find lambda from that factorization method old form calculator okay and if factorization there if it was easy you can find but for in some cases you have to use that e^x formula like plus minus B something like that or formula yes so first to be safe you can use calculator okay it will save your time and your you will get perfect answer also okay because because the answer of this question will be further we have to solve the equations and other things also yes for Higgins I better also we have to do not only this will give again values lambda will be if you use calculator you will get lambda 3 comma 1 two values will be their big three and one now let us push it therefore begin values 3 comma 1 ok you may thought for lambda cube there must be three values yeah one maybe double this way you can you have to take only two now let's proceed but we are we have find Egon Parris yes now we will move on for chicken factor even better it lambda equals to 3 at lambda equals to 3 we have a formula x equals to lambda X ok great the x equals 2 the x y and z XY jet and it goes to lambda x Oh to 1 1 1 to 1 to 0 1 this is a and for the X we have to write X Y Z equals to lambda into the XY saved that is pushing or 2x God's y+ said 1x plus 2 I gots it 0.2 X plus 0.1 plus jet because 2 and we might have like this that land up with will depress that lambda 3 and we'll get 3 X 3 y 3 gentle what we have before we have like this lambda into the XY Z it yes if lambda is 3 then 3 X 3 y 3 jet this will read yeah okay now we'll solve this equation here from top we go from top okay from top over there you see 2 X plus y plus Z goes to 3 X 4 and these three X will come here left side then we have minus 3x plus 3x minus X plus y cos it goes to 0 therefore the x equals 2y plus 0 we will use this equation now in the second equation we have also the X plus 2 I plus J 2 goes to 3 1 here during this second equation yes X plus 2 y plus 2 equals to 3 1 or Y ax and this 3 I will come here and minus 3 y plus 2 y minus y plus Z goes to 0 now poly X will replace with this value we have got the x equals 2y plus J and now we will replace this x value here or X means y plus jet and minus y plus Z goes to 0 ok what we get yeah here we have Y and minus y cancel or jet blast it to jet it goes to 0 that is jet it goes to now we put this jet equals to 0 in this first equation then we will get therefore the x equals 2y plus 0 therefore the x equals 2y if we get the x equals 2y then we don't need to find another way okay now we have same value of x and y we can write those in reacts term in again back to okay therefore you can back to will be right here therefore even better is yes okay the ax is equals to Y so in terms of Y also we write Y X B and again for jet we have here jets well jet equals to zero in this way we will get our Egan back sir you can write in whatever form you like in Y form also you can write like y equals 2x in that way you can write Y that's okay but if you write in terms of X it will be easy for you okay now for we are fine the even vector for three yes lambda equal to 3 we find your vector now again you can find with lambda equals to 3 also in this for lambda equals to 3 also we have to do in same method okay so I am doing this much video is also longer okay guys if you liked my video please subscribe my channel and don't forget to like thank you

Channel: ASP Hero

Views: 17,657

Rating: 4.0259066 out of 5

Keywords: learn maths, engineering mathematics, matrix, eigen value, eigen vector

Id: 1gAlA3WLk0o

Length: 23min 31sec (1411 seconds)

Published: Mon Jun 04 2018