what is the best way to find the basis of subspace V(x,y,z,w) which is an element of R^4 for 2x-y=z-3w
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Try constructing a matrix and row-reduce the matrix to find the number of free parameters. Then take that and construct a basis using the free parameters.
in this case are there 3 parameters?
you cant really row reduce ..so what now?please specify.thanks.
Originally Posted by n22 Hi,
what is the best way to find the basis of subspace V(x,y,z,w) which is an element of R^4 for 2x-y=z-3w This is the same as z= 2x- y+ 3w. Such a vector can be written as <x, y, z, w>= <x, y, 2x- y+3w, w>= <x, 0, 2x, 0>+ <0, y, -y, 0>+ <0, 0, 3w, w>= x<1, 0, 2, 0>+ y<0, 1, -1, 0>+ w<0, 0, 3, 1>.
From that it should be obvious what a basis is and what the dimension is.
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