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Linear Algebra Done Right (Undergraduate Texts in Mathematics) | 3rd Edition | ISBN: 9783319110790 | Authors: Sheldon Axler
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Show that the function that takes.x1; x2; x3/; .y1; y2; y3/2 R3 R3to x1y1 C x3y3 is not

Chapter 6, Problem 2

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QUESTION:

Show that the function that takes.x1; x2; x3/; .y1; y2; y3/2 R3 R3to x1y1 C x3y3 is not an inner product on R3.

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QUESTION:

Show that the function that takes.x1; x2; x3/; .y1; y2; y3/2 R3 R3to x1y1 C x3y3 is not an inner product on R3.

ANSWER:

Problem 2

Show that the function that takes  to  is not an inner product on .

                                            Step-by-step solution

Step 1 of 2

Consider the provided statement to show that the function that takes to   is not an inner product on .

As it is known that an inner product on  is a function that takes each ordered pair of elements of  to a number  and has the properties of positivity, definiteness, additivity in the first slot, homogeneity in the first slot and conjugate symmetry.

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