GIven set is not Linearly dependent hence not a basis. So should we take basis as {(1.0.0.0),(0,1,0,0),(0,0,1,0),(0,0,0,1)} and give as dim(R^4) = 4 or any other solution is expected?
2026-03-25 07:46:22.1774424782
Find the dimension of the subspace of R^4 spanned by the set {(1,0,0,0),(0,1,0,0),(1,2,0,1),(0,0,0,1)}. Hence find a basis for the subspace
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If you row reduce the matrix formed by these vectors (as lines), you'll be able to compute its rank (it is 3). This is the maximum number of linearly independent rows. So, you can just pick 3 linearly independent vectors from the subspace as its basis, for instance $(1,0,0,0), (0,1,0,0),(0,0,0,1)$.