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Consider the following statements: 1. If V = span{v,, v2, vn} then {v, v2, v} is a basis for V. 2. If V = span{vi , v2,, vn} then dim(V) < n. 3. Every linearly independent subset of a vector space is a basis. 4. If v, E span{v, v2,, Un-1} then span{vı, v2,,un} = span{v}, v2, ., Un-1}: 5. If , E span{vi, v2, .., Un-1} then {v1, v2, ., vn} is linearly dependent. Which of the following is true? A. Statements 1, 2 and 3 are true. B. Statements 1, 2 and 5 are true. OC. Statements 3, 4 and 5 are true. O D. Statements 2, 3 and 4 are true. O E. Statements 2, 4 and 5 are true.

Consider the following statements: 1. If V = span{v,, v2, vn} then {v, v2, v} is a basis for V. 2. If V = span{vi , v2,, vn} then dim(V) < n. 3. Every linearly independent subset of a vector space is a basis. 4. If v, E span{v, v2,, Un-1} then span{vı, v2,,un} = span{v}, v2, ., Un-1}: 5. If , E span{vi, v2, .., Un-1} then {v1, v2, ., vn} is linearly dependent. Which of the following is true? A. Statements 1, 2 and 3 are true. B. Statements 1, 2 and 5 are true. OC. Statements 3, 4 and 5 are true. O D. Statements 2, 3 and 4 are true. O E. Statements 2, 4 and 5 are true.

Linear Algebra: A Modern Introduction
Linear Algebra: A Modern Introduction
4th Edition
ISBN:9781285463247
Author:David Poole
Publisher:David Poole
Chapter1: Vectors
Section: Chapter Questions
Problem 20RQ
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Consider the following statements: 1. If V = span{v, V2, ..., vn} then {v1 , V2, ., vn} is a basis for V. 2. If V = span{vi , v2,, un} then dim(V) <n. 3. Every linearly independent subset of a vector space is a basis. 4. If v, E span{v, v2,., Vn-1} then span{vi, 02,, Un} = span{v, v2,., Un-1}. 5. If v, E span{vi, v2,., Un-1} then {vi, v2, .., Vn} is linearly dependent. Which of the following is true? O A. Statements 1, 2 and 3 are true. B. Statements 1, 2 and 5 are true. O C. Statements 3, 4 and 5 are true. O D. Statements 2, 3 and 4 are true. O E. Statements 2, 4 and 5 are true.
Transcribed Image Text:Consider the following statements: 1. If V = span{v, V2, ..., vn} then {v1 , V2, ., vn} is a basis for V. 2. If V = span{vi , v2,, un} then dim(V) <n. 3. Every linearly independent subset of a vector space is a basis. 4. If v, E span{v, v2,., Vn-1} then span{vi, 02,, Un} = span{v, v2,., Un-1}. 5. If v, E span{vi, v2,., Un-1} then {vi, v2, .., Vn} is linearly dependent. Which of the following is true? O A. Statements 1, 2 and 3 are true. B. Statements 1, 2 and 5 are true. O C. Statements 3, 4 and 5 are true. O D. Statements 2, 3 and 4 are true. O E. Statements 2, 4 and 5 are true.
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