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2. Consider a set of four non-zero vectors in $\mathbb{R}^4$ where the fourth vector is a linear combination of the first three vectors. Using the definition from this week, explain why this set of vectors cannot be linearly independent. (3 marks. Use complete sentences.) 3. Write the standard basis for $\mathbb{R}^5$. Prove that any vector in $\mathbb{R}^5$ can be written as a linear combination of the standard basis. (4 marks. Use complete sentences to make a convincing argument.)

          2. Consider a set of four non-zero vectors in $\mathbb{R}^4$ where the fourth vector is a linear combination of the first three vectors. Using the definition from this week, explain why this set of vectors cannot be linearly independent. (3 marks. Use complete sentences.)
3. Write the standard basis for $\mathbb{R}^5$. Prove that any vector in $\mathbb{R}^5$ can be written as a linear combination of the standard basis. (4 marks. Use complete sentences to make a convincing argument.)

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2. Consider a set of four non-zero vectors in ℝ^4 where the fourth vector is a linear combination of the first three vectors. Using the definition from this week, explain why this set of vectors cannot be linearly independent. (3 marks. Use complete sentences.)
3. Write the standard basis for ℝ^5. Prove that any vector in ℝ^5 can be written as a linear combination of the standard basis. (4 marks. Use complete sentences to make a convincing argument.)

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Elementary and Intermediate Algebra

Alan S. Tussy, R. David Gustafson 5th Edition

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Solved by Expert Uma Kumari

02/26/2022

Step 1

Step 1: To determine if a set of vectors is linearly independent, we need to check if the only solution to the equation c1v1 + c2v2 + c3v3 + c4v4 = 0 is c1 = c2 = c3 = c4 = 0, where v1, v2, v3, and v4 are the vectors in question. Show more…

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where the fourth vector is a linear combination of the first three vectors. Using the definition from this week, explain why this set of vectors cannot be linearly independent. (3 marks. Use complete sentences.) vector in IR5 can be written as a linear combination of the standard basis. (4 marks. Use complete sentences to make a convincing argument.)

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