Find the principal axes $y_{1}$ and $y_{2}$ diagonalizing the quadratic form $q = x_{1}^{2} + 8x_{1}x_{2} + x^{2}_{2} $. Please explain how to find the principle axis.
2026-03-27 15:20:13.1774624813
Find the principal axes $y_{1}$ and $y_{2}$ diagonalizing the quadratic form $q = x_{1}^{2} + 8x_{1}x_{2} + x^{2}_{2} $
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Hints:
What is the matrix representing the quadratic function? In other words, what is the real symmetric matrix you are working with?
How do you diagonalize it?