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Posted: **Mon Jul 11, 2022 11:15 am**

: 20 Let B Be A Basis For R Prove That The Vectors V V Vk Span R If And Only If The Vectors V B V B 1 (11.29 KiB) Viewed 31 times

: 20 Let B Be A Basis For R Prove That The Vectors V V Vk Span R If And Only If The Vectors V B V B 2 (14.75 KiB) Viewed 31 times

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20. Let B be a basis for R". Prove that the vectors V₁, V₂, ..., Vk span R" if and only if the vectors [V₂]B, [V₂]B,..., [VK]B span Rn.

21. Let B be a basis for R". Prove that the vectors V₁, V₂, ..., Vk form a linearly independent set in R" if and only if the vectors [V₁]B₂ [V₂]B... [VK]B form a linearly independent set in R".