Let W_1 be the set: [1 -3 0], [-2 9 0], [0 0 0], [0 -3 5]. Determine if W_1 is a

Question

Let W_1 be the set: [1 -3 0], [-2 9 0], [0 0 0], [0 -3 5]. Determine if W_1 is a basis for R^3 and check the correct answer(s) below. A. W_1 is not a basis because it is linearly dependent. B. W_1 is a basis C. W_1 is not a basis because it does not span R^3. Let W_2 be the set: [-2 3 0], [6 -1 5]. Determine if W_2 is a basis for R^3 and check the correct answer(s) below. A. W_2 is not a basis because it does not span R^3. B. W_2 is not a basis because it is linearly dependent. C. W_2 is a basis.

Explanation / Answer

W1 is not a basis of R3 since R3 is of dimension three.W1 contains 4 vectors.we know a result in an n dimensional vector space n+1 vectors are linearly dependent. So W1 is not linearly independent so it is not a basis for R3.

W2 is not a basis of R3 since R3 is of dimension 3, so its basis contain 3 linearly independent vectors.but W2 only contain two vectors so which cannot span R3 so W2 not a basis of R3.

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