Q11E TRUE OR FALSE?聽If x鈬赌and聽y鈬赌... [FREE SOLUTION]

91影视

Linear Algebra With Applications

Otto Bretscher

$Math Studyset 91影视 Explanations$ Math

5th Edition 路 442 pages

ISBN: 9780321796974

Chapter 5: Q11E (page 263)

TRUE OR FALSE?If $\overset{鈬赌}{x} a n d \overset{鈬赌}{y}$ are two vectors in $R^{n}$ , then the equation role="math" localid="1659506190737" $鈭� \overset{鈫�}{x} + \overset{鈫�}{y} {鈭�}^{2} = 鈭� \overset{鈫�}{x} {鈭�}^{2} + 鈭� \overset{鈫�}{y} {鈭�}^{2}$ must hold.

Short Answer

Expert verified

The given statement is false.

Step by step solution

Statement of a Pythagorean Theorem.

Suppose $\overset{鈬赌}{x} a n d \overset{鈬赌}{y}$ andare two vectors in $R^{n}$ .

Then the equationrole="math" localid="1659507544082" $鈭� \overset{鈫�}{x} + \overset{鈫�}{y} {鈭�}^{2} = 鈭� \overset{鈫�}{x} {鈭�}^{2} + 鈭� \overset{鈫�}{y} {鈭�}^{2}$ holds if and only ifandare orthogonal.

Check whether the given statement is a true or false.

The given statement is if $\overset{鈬赌}{x} a n d \overset{鈬赌}{y}$ and are two vectors in $R^{n}$ , then the equation role="math" localid="1659507570743" $鈭� \overset{鈫�}{x} + \overset{鈫�}{y} {鈭�}^{2} = 鈭� \overset{鈫�}{x} {鈭�}^{2} + 鈭� \overset{鈫�}{y} {鈭�}^{2}$ must hold.

By the Pythagorean Theorem, the equation $鈭� \overset{鈫�}{x} + \overset{鈫�}{y} {鈭�}^{2} = 鈭� \overset{鈫�}{x} {鈭�}^{2} + 鈭� \overset{鈫�}{y} {鈭�}^{2}$ is holds only when $\overset{鈬赌}{x}$ and $\overset{鈬赌}{y}$ are orthogonal.

Then the given statement is false.

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91影视

Short Answer

Step by step solution

Statement of a Pythagorean Theorem.

Check whether the given statement is a true or false.

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91影视

TRUE OR FALSE?If x鈬赌andy鈬赌are two vectors inRn, then the equation role="math" localid="1659506190737" 鈭�x鈫�+y鈫�鈭�2=鈭�x鈫�鈭�2+鈭�y鈫�鈭�2must hold.

Short Answer

Step by step solution

Statement of a Pythagorean Theorem.

Check whether the given statement is a true or false.

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Math Textbooks

Calculus

Theoretical and Mathematical Physics

Discrete Mathematics

Statistics

Mechanics Maths

Logic and Functions

Study anywhere. Anytime. Across all devices.