3A Given the Euclidean inner product space (R³(R),+,,*), where for each_x=(x1,X2,X3), y=(yı,y2,y)=R³, X*y = 2(x1y1+x3y3) + x2(y1+y3) + (x1+x3)y2 + 3x2y2. Check whether the matrix A of the inner product (*) is squared with respect to the natural basis of R³, without computing its eigenvalues and eigenvectors.

Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
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Chapter2: Second-order Linear Odes
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3A
Given the Euclidean inner product space (R³(R),+,,*), where for each_x=(X1,X2,X3),
y=(yı,y2,y3) ER³,
x*y = 2(x₁y1+x3y3) + X2(Y₁+Y3) + (x1+x3)y2 + 3x2y2.
Check whether the matrix A of the inner product (*) is squared with respect to the natural
basis of R³, without computing its eigenvalues and eigenvectors.
Transcribed Image Text:3A Given the Euclidean inner product space (R³(R),+,,*), where for each_x=(X1,X2,X3), y=(yı,y2,y3) ER³, x*y = 2(x₁y1+x3y3) + X2(Y₁+Y3) + (x1+x3)y2 + 3x2y2. Check whether the matrix A of the inner product (*) is squared with respect to the natural basis of R³, without computing its eigenvalues and eigenvectors.
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