Let W = {(x, y) E R² : x, y > 0}. Define addition + of any two elements (x, y), (w, z) E W by (х, у) + (w, z) %3D (хи, уz) where xw on the right-hand side denotes standard multiplication of the two real numbers x and w, and yz is interpreted similarly. Define scalar multiplication on W so that for all 1 E R and (x, y) E W we have a(x, y) = (x², y^) where x on the right-hand side denotes the standard operation of raising a positive real number to the power of another real number, and similarly for y. If 0 E W satisfies u + 0 = u for all u e W, then what must the second entry of 0 be? Answer:
Let W = {(x, y) E R² : x, y > 0}. Define addition + of any two elements (x, y), (w, z) E W by (х, у) + (w, z) %3D (хи, уz) where xw on the right-hand side denotes standard multiplication of the two real numbers x and w, and yz is interpreted similarly. Define scalar multiplication on W so that for all 1 E R and (x, y) E W we have a(x, y) = (x², y^) where x on the right-hand side denotes the standard operation of raising a positive real number to the power of another real number, and similarly for y. If 0 E W satisfies u + 0 = u for all u e W, then what must the second entry of 0 be? Answer:
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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Transcribed Image Text:Let W = {(x, y) E R² : x, y > 0}.
Define addition + of any two elements (x, y), (w, z) E W by
(x, y) + (w, z) = (xw, yz)
where xw on the right-hand side denotes standard multiplication of the two real numbers x
and w, and yz is interpreted similarly.
Define scalar multiplication on W so that for all å E R and (x, y) E W we have
1(x, y) = (x², y²)
where x1 on the right-hand side denotes the standard operation of raising a positive real
number to the power of another real number, and similarly for y^.
If 0 E W satisfies u + 0 = u for all u E W, then what must the second entry of 0 be?
Answer:
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