Let f(x) = xT Ax be a quadratic form with associated n X n symmetric matrix A. Let the eigenvalues of A be λ1 >= λ2>= ···>= λn  Then the following are true, subject to the constraint II x|| = 1: Prove The minimum value of f(x) is λn, and it occurs when x is a unit eigenvector corresponding to λn

Q: Using the attached theorms, Solve dx/dt =2x+4y , dy/dt=-x+6y

A: Reference: Differential Equations, Linear Algebra

Q: and find the corresponding eigenvector.

A: λ is an eigen value if we have Av=λv for some v non-zero.v is called eigen vector.

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A: according to guidelines we can solved only first 3 subparts thank you   We have the eigen values of…

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Q: 2. Suppose A is a square matrix and A² = [0] (the zero matrix). (a) Explain why X = 0 is the only…

A: A is a square matrix and A2=0(the zero matrix)

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