Determine if W1 is a basis for R3 and check the correct answer(s) below

Question

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Answer 1

W₁: Form the 3x3 matrix with the elements of W₁ as its columns. The matrix can be row reduced to the 3x3 identity matrix. So, the vectors in W₁ are linearly independent. Any set of 3 linearly independent vectors in lR³ is a basis of lR³.

W₂: If the elements of W₂ are put into a 3x3 matrix as its columns, the matrix can't be row reduced to the 3x3 identity matrix. So, the vectors in W₂ do not form a linearly independent set of 3 vectors in lR³. Consequently, W₂ is not a basis of lR³.