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Get Full Access to Linear Algebra And Its Applications - 5 Edition - Chapter 4.1 - Problem 30e
Get Full Access to Linear Algebra And Its Applications - 5 Edition - Chapter 4.1 - Problem 30e

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# Suppose cu = 0 for some nonzero scalar c. Show that u = 0.

ISBN: 9780321982384 49

## Solution for problem 30E Chapter 4.1

Linear Algebra and Its Applications | 5th Edition

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Problem 30E

Problem 30E

Suppose cu = 0 for some nonzero scalar c. Show that u = 0. Mention the axioms or properties you use.

Step-by-Step Solution:

Solution 30E

Step 1 of 2

Consider for some nonzero scalar c,

Need to show that,

Suppose a non-empty set of vectors, V is a vector space. Then, the following axioms must hold for all vectors in V, and, for all scalars, and, .

If  are in V, then, the sum of  denoted by, is in V.

, where zero 0, is a vector in V.

For each  in V, there exists a vectorin V, such that

For in V, and, for a scalar, the scalar multiple of by, is denoted by , is in.

Step 2 of 2

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