Algebra and Trigonometry (6th Edition)
Algebra and Trigonometry (6th Edition)
6th Edition
ISBN: 9780134463216
Author: Robert F. Blitzer
Publisher: PEARSON
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Let I2 € M₂(K) be the 2 × 2 identity matrix, where K is a field. For any A € M₂(K), let V₁ = 12, V₂ = A, V3 = A² and regard them as elements of V = M₂(K) as a vector space. [ 1 (i) Show that v₁, V2, V3 are linearly dependent as elements of V. Let K = R and A
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Transcribed Image Text:Let I2 € M₂(K) be the 2 × 2 identity matrix, where K is a field. For any A € M₂(K), let V₁ = 12, V₂ = A, V3 = A² and regard them as elements of V = M₂(K) as a vector space. [ 1 (i) Show that v₁, V2, V3 are linearly dependent as elements of V. Let K = R and A
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Step 1: Finding v3
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Step 2: Finding relation between the vectors
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Step 3: Conclusion
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Solution
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