Example of Linear Independence Using Determinant

Linear Algebra: Let S = {[12, 0, 4, 0], [3,1 , 1, 1], [3, 0, 2, 0], [3, 2, 0, 0]}. Show that S is a linearly independent set by computing the determinant of the matrix whose columns are the vectors in S.

[bikespike]

very straight forward, clearly explained and understood everything first pass . Thank you!

[srockerrr]

So very on point. Great, thank you so much!

[MathDoctorBob]

You're welcome! Glad to be of help.

[achrafelkassih]

thank u so much ....short and useful lecture :)

[MathDoctorBob]

@Fleckaveli You're welcome! Glad to be of help.

[truongdq]

thank you, It's really helpful. It help me to refresh my knowledge about linear algebra.

[MathDoctorBob]

@Fleckaveli Great job! Keep up the hard work yourself. If you have any requests for finals, let me know.

[MegaBdboy]

So this works just if the matrix is square ?And if the matrix is non square can we take the rank of the matrix and if is non 0, can we say that those vectors are linear independent ?

[viviannevilar]

It was very clear, thanks.

By the way, you look like a jiu-jitsu fighter :)

[MathDoctorBob]

@thejuggler1231 You're welcome! Thanks for the comment.

[MathDoctorBob]

@viviannevilar You're welcome! I could use less jiu-jitsu on the ears. - Bob

[alyaazahan]

i dont really understand those (-1)^(3+3) could u explain more?