4. State with a brief explanation whether the following statements are true or false. (a) The vectors (1,0) and (0, 1) span R². (b) The vectors (2,−1), (0, 1), and (1,0) span R². (c) The vectors (1,0) and (0, 1) are linearly independent. (d) The vectors (2, -1), (0, 1) and (1,0) are linearly independent. (e) A set of any two vectors in R² is a basis for R². (f) A set of any three vectors in R² must be linearly dependent. (g) R2 is a subspace of R³.

4. State with a brief explanation whether the following statements are true or false. (a) The vectors (1,0) and (0, 1) span R². (b) The vectors (2,−1), (0, 1), and (1,0) span R². (c) The vectors (1,0) and (0, 1) are linearly independent. (d) The vectors (2, -1), (0, 1) and (1,0) are linearly independent. (e) A set of any two vectors in R² is a basis for R². (f) A set of any three vectors in R² must be linearly dependent. (g) R2 is a subspace of R³.

Advanced Engineering Mathematics

10th Edition

ISBN:9780470458365

Author:Erwin Kreyszig

Publisher:Erwin Kreyszig

Chapter2: Second-order Linear Odes

Section: Chapter Questions

Problem 1RQ

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