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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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![12. Suppose that \( T : V \rightarrow W \) and \( S : V \rightarrow W \) are linear transformations, \( \alpha \) is a basis for \( V \), and \( \beta \) is a basis for \( W \). Show that:
a) \([T + S]_{\alpha}^{\beta} = [T]_{\alpha}^{\beta} + [S]_{\alpha}^{\beta}\).
b) If \( c \) is a scalar, \([cT]_{\alpha}^{\beta} = c[T]_{\alpha}^{\beta}\).](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fbfa44710-6742-4cf8-9a38-b63fd4325c9b%2F5d4f9c22-207e-4c8c-a12c-1e7ab731a6c8%2Fo286lyh_processed.jpeg&w=3840&q=75)
Transcribed Image Text:12. Suppose that \( T : V \rightarrow W \) and \( S : V \rightarrow W \) are linear transformations, \( \alpha \) is a basis for \( V \), and \( \beta \) is a basis for \( W \). Show that:
a) \([T + S]_{\alpha}^{\beta} = [T]_{\alpha}^{\beta} + [S]_{\alpha}^{\beta}\).
b) If \( c \) is a scalar, \([cT]_{\alpha}^{\beta} = c[T]_{\alpha}^{\beta}\).
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