Inverse of 4x4 Matrix Using Row Operations

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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.

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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

MathDoctorBob

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

MaXXie

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

yuvrajmalik

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.

MathDoctorBob

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

MathDoctorBob

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..

QwertyQwerty-sokw

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

tadas

@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

MathDoctorBob

math doctor bob more like plague doctor bob

archsprite

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

praiseayorinde

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

yeehaaaaaaw

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

MathDoctorBob

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

wesamelmansour

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

biswajitojha

Thanks for the help. Worked out great.

BessieMorrison

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

jamesekeenan

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

yeehaaaaaaw

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

nicechinwo

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

anuragyadav

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

annshiro

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