17. а. х — 0, у30, z%3D0 ь. х2 0, у 0, Z %3D0 18. a. 0 1 b. x? + y? < 1, z = 3 b. x? + y? + z? < 1, z 2 0 b. х%3D у, b. x s y², 0 s 2 no restriction on z 23. а. у 2 х?, 20 24. a. z = 1 – y, no restriction on x b. z = y, x = 2

Linear Algebra: A Modern Introduction
4th Edition
ISBN:9781285463247
Author:David Poole
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Chapter5: Orthogonality
Section5.3: The Gram-schmidt Process And The Qr Factorization
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In Exercises 17–24, describe the sets of points in space whose coordinates satisfy the given inequalities or combinations of equations and inequalities.

17. а. х — 0, у30, z%3D0 ь. х2 0, у 0, Z %3D0
18. a. 0 <x <1
b. 0 sx< 1, 0 sys1
c. 0 <xs 1, 0 s ys 1, 0s
19. а. х? + у? + z? s 1
20. a. x2 + y? < 1, z = 0
c. x² + y? < 1, no restriction on z
21. a. 1<x + y? + z? < 4
22. а. х 3D у, %3D0
b. x? + y? + z? > 1
b. x? + y? < 1, z = 3
b. x? + y? + z? < 1, z 2 0
b. х%3D у,
b. x s y², 0 s 2
no restriction on z
23. а. у 2 х?, 20
24. a. z = 1 – y, no restriction on x
b. z = y, x = 2
Transcribed Image Text:17. а. х — 0, у30, z%3D0 ь. х2 0, у 0, Z %3D0 18. a. 0 <x <1 b. 0 sx< 1, 0 sys1 c. 0 <xs 1, 0 s ys 1, 0s 19. а. х? + у? + z? s 1 20. a. x2 + y? < 1, z = 0 c. x² + y? < 1, no restriction on z 21. a. 1<x + y? + z? < 4 22. а. х 3D у, %3D0 b. x? + y? + z? > 1 b. x? + y? < 1, z = 3 b. x? + y? + z? < 1, z 2 0 b. х%3D у, b. x s y², 0 s 2 no restriction on z 23. а. у 2 х?, 20 24. a. z = 1 – y, no restriction on x b. z = y, x = 2
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