The vectors (1,2,3,4),(0,1,2,3),(0,0,1,2),(0,0,0,1) creates a basis in R^4. Decide the coordinates for the vector (1,1,1,1) in the given basis.

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- anonymous

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- anonymous

The answer is (1,-1,0,0) however I don't know how to get there.

- anonymous

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- anonymous

i hope that helps, all u need is a vectors that u can multiply the basis with to get [1 1 1 1]

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- anonymous

vector*

- anonymous

Ohh I see, thank you very very much! :)

- anonymous

Excuse me, why do we use row vectors instead of column vectors in this case? Are the two the same?

- anonymous

actually, the basis is given to us, so we dont need to find it, but if we were to find it then we have to put the vectors in columns.... frx gave the basis as row vectors, the question was not in proper notation

- anonymous

Does that mean when we do this question, we put the vectors in rows, since the given vectors are row vectors. When the given vectors are column vectors, when we need to put it in columns?
I'm sorry, I'm quite confused.

- anonymous

Also, how do you find the B for \(B \cdot A\)?
And.... Why is the multiplication correct? I mean B is a 1x4 matrix and A is a 3x4 matrix. How can we find the matrix product \(B \cdot A\)?

- anonymous

matrix multiplication works like that.... matrices dont need to be the same size to multiply dem

- anonymous

check out example 1 here: http://www.mathwarehouse.com/algebra/matrix/multiply-matrix.php

- anonymous

The problem is that for matrix multiplication, we need the number of columns of the first matrix equal to the number of rows of the second matrix. But in your working, B is a 1x4 matrix, while A is a 3x4 matrix. The number of columns of B is not equal to the number of rows of A, so, I think the matrix multiplication is undefined.

- anonymous

A is a 4x4 matrix... take a look at it again, u didnt see it right

- anonymous

I see the problem now... The first matrix A is a 4x4 matrix. But when you write BA, the matrix A there is of the size 3x4. You missed the third row there. I was looking at that BA, and didn't realise that you missed a row there. Sorry!!!

- anonymous

ohhh yes, i did miss a row, sorry

- anonymous

Thanks a lot though! I understand how to do this question now :)

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