IIT JEE , AIEEE Forum - Mathematics , Algebra

nasa_hs

whats eigen values of a nonsingular matrix? n d q goes like thi.........iF 3.-2 r d EIGEN values of a non-singular matrix A & IAI=4 then the eigen values of adjA r ?

ans is 4/3,-2

n whats rank of a matrix??????

RyuAmakusa

check
http://www.goiit.com/posts/list/integration-please-do-show-the-method-of-solving-55111.htm#276259

mukundmadhav

Rank of a matrix is the maximum order of linearly independent rows or columns of a matrix. Eigen values of a matrix are the numerical values that satisfy the characterstic equation of a matrix. You can find eigen values of a matrix by subtracting x from the diagonal elements of a matrix and solving the determinant. The roots of the quadratic/ cubic(For 2 and 3 order matrix resp) are the eigenvalues of the matrix

magiclko

Consider the square matrix A . We say that $\lambda$ is a eigen vectorof A if there exists a non-zero vector x such that $AX =\lambda X$ . In this case, X is called an eigen vector(corresponding to eigen value $\lambda$ ),

$AX =\lambda X$

=> $(A-\lambda I) X = 0$

whr I is the identity matrix.. nd the solution to above is given by $det(A- \lambda I) = 0$

this equation is known as characterstic equation..nd the value of lambda are called the eigen values...of the matrix

PS: this all is not in JEE syllabus...

mukundmadhav

Characterstic equation is in the syllabus, so I think they can ask questions from eigenvalues too, right?

magiclko

no they cant, its Btech 1st yr's syllabus!!

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