[Math] Finding the dimension of a vector space

linear algebra

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I have done part i by putting $v_1,v_2,v_3,v_4$ into a matrix and the putting that matrix intro REF to find value of constants $c_1$ to $c_4$

But for the next part how do i find the dimension of $W$ and a basis for $W$?
(Also in general how do you find the dimension of a vector space)

Any help would be much appreciated.

Best Answer

Instead of putting $v_1,v_2,v_3,v_4$ as columns of the matrix, assume $v_1,v_2,v_3,v_4$ to be row vectors so that $v_1$ forms the first row of the matrix and so on. Now reduce the matrix to it's row echelon form. The number of non-zero rows is the dimension of W. And the non zero rows would form a basis of W.

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