Obtain the eigenvalues and the corresponding eigenvectors of the matrix:
b) Diagonalized the matrix:
The eigenvalues of A are: λ1 = 2, λ2 =1 and λ3 = -1.
c) Show that gij is a contravariant tensor of rank 2.
d) Show that the vectors are linearly independent.
### (a) Eigenvalues और Eigenvectors निकालें: दिए गए मैट्रिक्स \( A = \begin{bmatrix}-2 & 5 & _______ _____ ___ __________ _____ _____ ______ _______ ________ ___ __________.
________ ________ ______ ___ _____ _______ ________ __________ _________ _______ ____ ___.
_______ _______ __________ ___ _______ ___ ________ _________.
______ _____ __________ ___ ____.
____ _________ ____ ___ _____ __________ ______ _______ __________ _______.
________ ___ ___ __________ _____ ________ _________ _________.
____ ____ ________ ___ _____.
_______ _____ _________ _______ ___ ________.
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Using separation of variables, solve:
where
Show that the vectors are linearly independent.
Obtain the eigenvalues and the corresponding eigenvectors of the matrix:
b) Diagonalized the matrix:
The eigenvalues of A are: λ1 = 2, λ2 =1 and λ3 = -1.
c) Show that gij is a contravariant tensor of rank 2.
d) Show that the vectors are linearly independent.
Using the Laplace transforms, solve the following initial value problem:
where
Using recurrence relation, show that
where Jn(x) is the Bessel function of the first kind.
Determine the Fourier transform of the normalized Gaussian distribution
Show that a cyclic group is abelian.