maths ass2 - KAKATIYA INSTITUTE OF TECHNOLOGY SCIENCE WARANGAL(An Autonomous Institute under Kakatiya University Warangal Department Mathematics

maths ass2 - KAKATIYA INSTITUTE OF TECHNOLOGY SCIENCE...

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KAKATIYA INSTITUTE OF TECHNOLOGY & SCIENCE, WARANGAL (An Autonomous Institute under Kakatiya University, Warangal) Department Mathematics & Humanities Engineering Mathematics-IV ASSIGNMENT-II Date of posting: 25.12.2016 Last date for submission: 06.01.2017 5 X 1=5 1. Test for consistency 2 x  y  z , 3 x  y  3 z  2, 2 x  19 y  47 z  32 2.Determine the Eigen values of the matrix 2 1 4 5 . 3. State the Cayley-Hamilton theorem . 4. Verify the Cayley-Hamilton theorem for the matrix 2 3 4 1 . 5.Define Quadratic form and Canonical form of a matrix.. 5 X 2 =10 6. Test for consistency and solve the following system of equations x  y  z  3, 3
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Unformatted text preview: x y 2 z 1, 2 x 2 y 3 z 2, x y z 1. 7. Find the value of for which the system of equations 3 x y z 3 , x y z -2, 6 x y z 3 will have infinite no. of solutions . 8. Find the Eigen values and the corresponding Eigen vectors of the matrix 2 2 2 1 2 1 9. Verify the Cayley-Hamilton theorem and find it’s inverse 3 1 1 1 2 2 1 10. Diagonalize the Matrix A = 1 2 1 1 3 1 1 2 2...
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  • Spring '17
  • anandhmishra
  • Linear Algebra, eigen values, cayley-hamilton theorem, KAKATIYA INSTITUTE OF TECHNOLOGY

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