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Suppose the following three conditions are satisfied: (i) v1, v2, 03, w are linearly independent. (ii) v1, v2, v3, ž are linearly independent. (ii) v1 , v2, v3, w, ž are linearly dependent. Which of the following statements must be true? (Select all that apply)

Suppose the following three conditions are satisfied: (i) v1, v2, 03, w are linearly independent. (ii) v1, v2, v3, ž are linearly independent. (ii) v1 , v2, v3, w, ž are linearly dependent. Which of the following statements must be true? (Select all that apply)

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Suppose the following three conditions are satisfied: (i) v1, v2, V3, ủ are linearly independent. (ii) V1, V2, V3, ż are linearly independent. (iii) v1, v2, 03 , w, ž are linearly dependent. Which of the following statements must be true? (Select all that apply) span( v1, v2, 03, w) = span(71, 02, V3, Ž ) is a scalar multiple of z. W span( v1, 02, 03, w) = span( 71, v2, V3, ủ, ž) span( v1, v2, v3) = span( v1, v2, 03, w O span( 71, 02, v3) = span( v1, v2, 03, z) O 01, v2, vz are linearly independent.
Transcribed Image Text:Suppose the following three conditions are satisfied: (i) v1, v2, V3, ủ are linearly independent. (ii) V1, V2, V3, ż are linearly independent. (iii) v1, v2, 03 , w, ž are linearly dependent. Which of the following statements must be true? (Select all that apply) span( v1, v2, 03, w) = span(71, 02, V3, Ž ) is a scalar multiple of z. W span( v1, 02, 03, w) = span( 71, v2, V3, ủ, ž) span( v1, v2, v3) = span( v1, v2, 03, w O span( 71, 02, v3) = span( v1, v2, 03, z) O 01, v2, vz are linearly independent.
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