Let A be a 2×2 symmetric matrix. Show that if det A > 0 and trace(A)...

Let A be a 2×2 symmetric matrix. Show that if det A > 0 and trace(A) > 0 then A is positive definite. (trace of a matrix is sum of all diagonal entires.)

Expert Solution

milcah answered 2 years ago

Obtain a spectral decomposition for the symmetric matrix A = [0 2 2, 2 0 2,...

Obtain a spectral decomposition for the symmetric matrix A = [0 2 2, 2 0 2, 2 2 0] (that means the first row is 022, then below that 202, etc.) , whose characteristic polynomial is −(λ + 2)^2 (λ − 4) If you could provide a step-by-step way to solve this I'd greatly appreciate it.

Show that the hat matrix is idempotent (i.e. by showing that ?2 = ?) and symmetric.

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b) a matrix is skew symmetric if AT=-A.If A is a skew-symmetric matrix of odd order,show that A is not invertible c)Let A and B be n*n matrixes with detA=detB not equal to 0,If a and b are non zero real numbers show that det (aA+bB-1)=det(aB+bA-1)

Q. Let A be a real n×n matrix. (a) Show that A =0 if AA^T =0....

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Consider A, B and C, all nxn matrices. Show that: 1) det(A)=det(A^T) 2) if C was...

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Let A ∈ Mat n×n(R) be a real square matrix. (a) Suppose that A is symmetric,...

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Let A be an n × n real symmetric matrix with its row and column sums...

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