Inverse of 4x4 Matrix Using Row Operations

Linear Algebra: We find the inverse of a real 4x4 matrix using row operations. We note the bookkeeping pattern and check the answer with the equation A^-1 A = I.

[@MathDoctorBob]

Thanks! The long way: put it into row echelon form. If 4 pivots, then invertible. If less, not invertible. The quick(er) way: find the determinant. If = 0, not invertible. Otherwise invertible. - Bob

[@Jiglo]

4x4 matrixes hurt my brain.

[@tadas1233]

When you swapped the rows, didnt you have to change the sign? Or is it this applies only for determinants?

[@archsprite]

math doctor bob more like plague doctor bob

[@MathDoctorBob]

You're welcome! Fortunately these things are easy to program.

[@MaXXie007]

Thankyou- an easy explanation that is far quicker than using adjugates and doesnt require using the products of the row operators!

[@MathDoctorBob]

That's a determinant rule. If you think of the rows as linear equations by pulling apart AX = I, all we are doing is rearranging the order they are listed in.

[@wayo4662]

Helped me in 2021

[@MathDoctorBob]

I remember watching Family Matters unironically when it first aired.

[@Mulkek]

Thanks, and explain so clearly!

[@yuvrajmalik7997]

Amazing video. Helped me a lot. Thanks! You have no idea how much you've helped me.

[@George_Nakhle]

Thanks, this helped a lot

[@MathDoctorBob]

You're welcome! Good luck with exams. - Bob

[@praiseayorinde1791]

wow thank you so much, this is the first one I actually get

[@MathDoctorBob]

@MaXXie007 You're welcome! Actually the row operator matrices are hidden in the technique. That's why we perform the row operation on the entire row - RAB = RI. - Bob

[@elienezerothiniel4449]

10 years duuuh math live longer

[@lalithkumar9807]

Awesome sir

[@biswajitojha2600]

Thank you sir ☺️it helped me a lot and saved my time

[@MathDoctorBob]

Your welcome, and good luck with finals!

[@MathDoctorBob]

@jamesekeenan You're welcome! If you have any questions, I'm happy to help. Good luck and happy 2012! - Bob

[@MathDoctorBob]

You're welcome!

[@lesilaubarak2574]

Great work, you really help

[@QwertyQwerty-so4kw]

A lot of thx sir. Especially for the pattern u have given which made it so simple to solve as we now know the direction we are heading..

[@tadas1233]

right... thanks ;)

[@wesamelmansour5489]

what fast method to estimate inverse of matrix 4*4 or 5*5 by hand without using computer

[@yeehaaaaaaw]

ok sweet thanks. keep up the great videos man - if it wasn't for you i doubt i would have a passing grade in calc II

[@MathDoctorBob]

You're welcome! - Bob

[@zedlepplin9450]

thanks

[@yeehaaaaaaw]

great video bob, but i have a question for you. How can you tell if a 4x4 matrix is not invertible?

[@annshiro9532]

i dont know wat I'll do to understand!???

[@harderhscmaths]

Thanks Bob that is a nice method.

[@aysuoncu533]

thank youuuuuuuuuuuuu

[@BessieMorrison]

Thanks for the help. Worked out great.

[@jamesekeenan]

Thank you, I have some confidence now for my exam in January

[@nicechinwo1193]

please how can I find the inverse of an 8x8 matrix

[@MathDoctorBob]

By hand, it will need to be mostly zeros. Otherwise MAPLE (or another math software) is your friend.

[@anuragyadav587]

Sir, how do i check my answer?? Is there any method ?

[@lalithkumar9807]

Multiply the obtained matrix with the matrix u started with. if u get an identity matrix then ur answer is correct

[@duncanross4741]

awesome, thank you! *subscribes*