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DEPARTMENT OF MATHEMATICS& AS, MAD1181– ALGEBRA AND DIFFERENTIAL CALCULUS, PTA - MODULE I - MATRICES, PART-A, Find the sum of the squares of the eigen values of, Find the eigen values of A3 given A=, The characteristics equation of a matrix A is λ2 – 3 =0.What is A3?, Find the eigen values of 4A, given that A = has 2,2,2 as its Eigen values., Find the sum and product of all the eigen values of the matrix, If 3 and 15 are two eigen values of . What is the 3rdEigen value?, Find the eigen values of the matrix., Find the eigen values of A2 and A -1, if ., Find the eigen values of 3A2 if ., Find the Eigen value of adj(A), if ., Find the sum of Eigen values of 2A, if ., Find the sum and product of all eigen values of the matrix ., If 3 and 15 are the Eigen values of , Find without expanding the determinant., Two Eigen Values of are equal and they are double of the third. Find the Eigen values of A2., If , then find the eigenvalues of ., Write down the matrix of the quadratic form., Find the Quadratic form corresponding to the matrix., Determine the nature of the following quadratic form., PART-B, Find the eigen values and eigen vectors of the following matrices, (i) (ii) (iii) (iv) ., Verify Cayley Hamilton theorem and hence find the values of A4 and A-1for , A = (i) (ii) (iii) (iv) ., Diagonalize the following matrices (A) by orthogonal transformation and hence find A4, (i) (ii) (iii) (iv)., Reduce the following Quadradic Forms to Canonical Form by an orthogonal transformation. Also find the Rank, Index, Signature and Nature., (i) ., (ii) ., (iii) ., (iv) .