- Which of the following formulas define norms on R²? (Let (x, y) be the co- ordinates in R².) (a) (x² + xy + y²) ¹/²; (c) (x+y |) ²; (b) (d) (x²− 3xy + y²) ¹/²; 1/2 (x+| y |) + ¾/3 (x² + y²) ¹/².

Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
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6. Which of the following formulas define norms on R²? (Let (x, y) be the co-
ordinates in R².)
(a) (x² + xy + y²) ¹/2;
(c)
(| x | + | y |) ²;
(b)
(d)
(x²3xy + y²) ¹/2;
1/2
(x +| y |) + ³ (x² + y²) ¹/².
Transcribed Image Text:6. Which of the following formulas define norms on R²? (Let (x, y) be the co- ordinates in R².) (a) (x² + xy + y²) ¹/2; (c) (| x | + | y |) ²; (b) (d) (x²3xy + y²) ¹/2; 1/2 (x +| y |) + ³ (x² + y²) ¹/².
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