Linear Algebra Quiz
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EIGENVALUES & EIGENVECTORS
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For the quadratic form Q(x,y,z)=2x2+3y2+z2+4xy−2xz+6yzQ(x,y,z) = 2x^2 + 3y^2 + z^2 + 4xy - 2xz + 6yz, suppose we want to eliminate all cross-product terms by rotating to principal axes. If the coefficient matrix has eigenvalues λ1=6\lambda_1 = 6, λ2=3\lambda_2 = 3, and λ3=−3\lambda_3 = -3, what type of quadric surface does the equation Q(x,y,z)=18Q(x,y,z) = 18 represent?
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