Problem 1 (a). Consider the function 1 x1 F ([22₂]) = 3² ]) = 3x² + 2x1x2 + 2x². x2 Write down the bilinear transformation SA(, ) determined by the matrix A = HF, expressing your answer as a function of x1, x2, Y₁, Y2 (i.e. of the entries of and y). Show that SA is an inner product on R². Problem 1 (b). Compute the length of the vector = 3 [³] relative to A.
Problem 1 (a). Consider the function 1 x1 F ([22₂]) = 3² ]) = 3x² + 2x1x2 + 2x². x2 Write down the bilinear transformation SA(, ) determined by the matrix A = HF, expressing your answer as a function of x1, x2, Y₁, Y2 (i.e. of the entries of and y). Show that SA is an inner product on R². Problem 1 (b). Compute the length of the vector = 3 [³] relative to A.
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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![Problem 1 (a). Consider the function
1
x1
F ([22₂]) = 3²
]) = 3x² + 2x1x2 + 2x².
x2
Write down the bilinear transformation SA(, ) determined by the matrix
A = HF, expressing your answer as a function of x1, x2, Y₁, Y2 (i.e. of the
entries of and y). Show that SA is an inner product on R².
Problem 1 (b). Compute the length of the vector =
3
[³]
relative to A.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fac4b1575-c59a-4f97-bf1e-010a92525749%2Fdb842595-bcdd-4018-9b38-627bc2856983%2Ft7dfxwe_processed.png&w=3840&q=75)
Transcribed Image Text:Problem 1 (a). Consider the function
1
x1
F ([22₂]) = 3²
]) = 3x² + 2x1x2 + 2x².
x2
Write down the bilinear transformation SA(, ) determined by the matrix
A = HF, expressing your answer as a function of x1, x2, Y₁, Y2 (i.e. of the
entries of and y). Show that SA is an inner product on R².
Problem 1 (b). Compute the length of the vector =
3
[³]
relative to A.
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