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
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
Transcribed Image Text: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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