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Math / Linear Algebra 4 / Chapter 1.6 / Problem 11

Linear Algebra | 4th Edition | ISBN: 9780130084514 | Authors: Stephen H. Friedberg, Arnold J. Insel, Lawrence E. Spence

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Let u, v, and w be distinct vectors of a vector space V. Show that if {u, v, w} is a

Chapter 1, Problem 11

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QUESTION:

Let u, v, and w be distinct vectors of a vector space V. Show that if {u, v, w} is a basis for V, then {u 4- v 4- w, v + w, w} is also a basis for V.

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QUESTION:

Let u, v, and w be distinct vectors of a vector space V. Show that if {u, v, w} is a basis for V, then {u 4- v 4- w, v + w, w} is also a basis for V.

ANSWER:

Step 1 of 3

Let u, v, and w be distinct vectors of a vector space V such that .

If is a basis for V then, will also be the basis for V.

The proof as follows:

Let be a basis for V. Then, V will be a three-dimensional vector space and the linear combination is;

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