Basis for a Set of Vectors
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Basis for a Set of Vectors. In this video, I give the definition for a apos; basis apos; of a set of vectors. I think proceed to work an example that shows three vectors that I picked form a basis for R_3.
Comments
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east or west patrick is the best
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How does it look like when the vectors don't span? Is the system of linear equations inconsistent or does it have infinite many solutions?
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Patrick. don't you need to RREF before finding a_1 a_2 and a_3?
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for linear independence, can I have row1-row3 and make it my new row 2? or does it have to be row1-r0w3 and become the new row3 or row1?
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You can prove that they are basis using the determinant of the matrix formed by these vectors..
If the determinant is different than zero then the matrix is invertible hence by the equivalence theorem it only has the trivial solution and Ax=b is consistent ( A is the matrix formed by the vectors ) ... -
are 3x2 matrix have the determinant?
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what is trivial solution?
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thank for healping me
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could you have just taken the determinant of the 3 vectors to check if its linearly independent?
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thank you... for these videos :)
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Sorry guys, but if you're reading this can you explain some more ? I thought that you can tell that the vectors were linearly independent if you the row has a pivot (leading entry 1) why is he simplifying the matrix so much and making it equal to zero ? sorry question might sound stupid but I'm kind of confused
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so what happens when they are linearly dependant? that means that there's no basis?
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hey! thanks a lot that was very helpfull
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procedure for Column Space of a matrix is same as finding Basis for a set of vectors?
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I dont get it,if we prove that vectors are independent why do we have to prove that they span some space?Isnt it obvious if a set is independent that we can use linear combination of them to get some other vector from that space?Cheers
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Sir you deserve a Noble Prize for teaching poor kids like me.
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Is there any easier way to say: some vectors can span Rn ?
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So what, getting the equations for a1, a2, and a3 automatically shows that the vectors span R3? So when wouldn't they span R3?
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I usually do not comment on any of the videos but thanks a lot! this is great :D - From S. Korea
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Can't you just say that since the reduced matrix has a pivot in every row, the vectors span R3?
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