Linear algebra Consider the bilinear form H: R2 × R2 → R defined byY2H((r). ("))= x1 y1 + 6x1Y2+6x2Y1 + 3x2Y2.Let B =1{(2), (19)}-2be an ORDERED basis of R2, and let the matrix representationa11 a12(aof H with respect to the ordered basis ß be 1/3 (H) = (a21a22Then, a11a22a12a21

Given the bilinear form defined by.The ordered basis of R2 is .

Consider the bilinear form H: R2 × R2 R defined by →> = x1 y1 + 6x1y2+6x2Y1 + 3x2Y2. H Let B= = ((2), (")) = {(2)·(9)} of H with respect to the ordered basis ẞ be ³ (H) = (a a12 a21 a22 be an ORDERED basis of R2, and let the matrix representation

Consider the bilinear form H: R2 × R2 R defined by →> = x1 y1 + 6x1y2+6x2Y1 + 3x2Y2. H Let B= = ((2), (")) = {(2)·(9)} of H with respect to the ordered basis ẞ be ³ (H) = (a a12 a21 a22 be an ORDERED basis of R2, and let the matrix representation

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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Question

Linear algebra

Consider the bilinear form H: R2 × R2 → R defined by
Y2
H
((r). ("))
= x1 y1 + 6x1Y2+6x2Y1 + 3x2Y2.
Let B =
1
{(2), (19)}
-2
be an ORDERED basis of R2, and let the matrix representation
a11 a12
(a
of H with respect to the ordered basis ß be 1/3 (H) = (
a21
a22
Then, a11
a22
a12
a21

Branch of mathematics concerned with mathematical structures that are closed under operations like addition and scalar multiplication. It is the study of linear combinations, vector spaces, lines and planes, and some mappings that are used to perform linear transformations. Linear algebra also includes vectors, matrices, and linear functions. It has many applications from mathematical physics to modern algebra and coding theory.

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