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,...

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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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Find a matrix P that diagonalizes the matrix A = [ 2 0 ?2 / 0 3 0 / 0 0 3 ] and compute P ?1AP.

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