Let R² have the inner product (u,v) = 5u₁V₁ + 4u₂V2, and let x = (2,2) and y = (4, − 1). a. Find ||x||, ||y||, and | (x,y) |². b. Describe all vectors (Z₁,z₂) that are orthogonal to y. a. Find ||x||, ||y||, and | (x,y)|². ||x|| = (Simplify your answer. Type an exact answer, using radicals as needed.) (Simplify your answer. Type an exact answer, using radicals as needed.) ||y|| | (x,y) |² = (Simplify your answer.) b. Describe all vectors (z₁,z₂) that are orthogonal to y. Choose the correct answer below. = O A. All multiples of (-1,5) are orthogonal to y. B. All multiples of (1,5) are orthogonal to y. C. All multiples of (1, −5) are orthogonal to y. D. The zero vector is the only vector orthogonal to y.
Let R² have the inner product (u,v) = 5u₁V₁ + 4u₂V2, and let x = (2,2) and y = (4, − 1). a. Find ||x||, ||y||, and | (x,y) |². b. Describe all vectors (Z₁,z₂) that are orthogonal to y. a. Find ||x||, ||y||, and | (x,y)|². ||x|| = (Simplify your answer. Type an exact answer, using radicals as needed.) (Simplify your answer. Type an exact answer, using radicals as needed.) ||y|| | (x,y) |² = (Simplify your answer.) b. Describe all vectors (z₁,z₂) that are orthogonal to y. Choose the correct answer below. = O A. All multiples of (-1,5) are orthogonal to y. B. All multiples of (1,5) are orthogonal to y. C. All multiples of (1, −5) are orthogonal to y. D. The zero vector is the only vector orthogonal to y.
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 R² have the inner product (u,v) = 5u₁V₁ + 4u₂V2, and let x = (2,2) and y = (4, − 1).
a. Find ||x, y, and (x,y) |².
b. Describe all vectors (z₁,z₂) that are orthogonal to y.
a. Find ||×||, ||y||, and | (x,y)|².
||x||
=
(Simplify your answer. Type an exact answer, using radicals as needed.)
(Simplify your answer. Type an exact answer, using radicals as needed.)
=
||||
| (x,y) |² =
(Simplify your answer.)
b. Describe all vectors (z₁,z₂) that are orthogonal to y. Choose the correct answer below.
O A. All multiples of (-1,5) are orthogonal to y.
B. All multiples of (1,5) are orthogonal to y.
C. All multiples of (1, −5) are orthogonal to y.
D. The zero vector is the only vector orthogonal to y.
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