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8. a. Consider a linear transformation T from R° to R'. What are the possible values of dim(ker T)? Explain. b. Consider a linear transformation T from R4 to R'. What are the possible values of dim(imT)? Explain.

8. a. Consider a linear transformation T from R° to R'. What are the possible values of dim(ker T)? Explain. b. Consider a linear transformation T from R4 to R'. What are the possible values of dim(imT)? Explain.

Advanced Engineering Mathematics
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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**38.** **a.** Consider a linear transformation \( T \) from \( \mathbb{R}^5 \) to \( \mathbb{R}^3 \). What are the possible values of \( \dim(\ker T) \)? Explain. **b.** Consider a linear transformation \( T \) from \( \mathbb{R}^4 \) to \( \mathbb{R}^7 \). What are the possible values of \( \dim(\mathrm{im} T) \)? Explain.
Transcribed Image Text:**38.** **a.** Consider a linear transformation \( T \) from \( \mathbb{R}^5 \) to \( \mathbb{R}^3 \). What are the possible values of \( \dim(\ker T) \)? Explain. **b.** Consider a linear transformation \( T \) from \( \mathbb{R}^4 \) to \( \mathbb{R}^7 \). What are the possible values of \( \dim(\mathrm{im} T) \)? Explain.
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