dyGPTQuestion textWhat is an eigenvector of a matrix?Question 6Answera.A vector that changes magnitude under the associated linear transformationb.A vector that does not change direction under the associated linear transformationc.A vector that changes direction under the associated linear transformationd.A vector that is orthogonal to the transformation matrix

Which of the following statement(s) is/are true with respect to eigenvalues andeigenvectors of a matrix?(A) The sum of the eigenvalues of a matrix equals the sum of the elements of theprincipal diagonal.(B) If is an eigenvalue of a matrix A, then1 is always an eigenvalue of itstranspose (AT).(C) If is an eigenvalue of an orthogonal matrix A, then1 is also an eigenvalue ofA.(D) If a matrix has n distinct eigenvalues, it also has n independent eigenvectors.Q.30 For studying wing vibrations, a wing of mass M and finite dimensions has beenidealized by assuming it to be supported using a linear spring of equivalentstiffness k and a torsional spring of equivalent stiffnessk as shown in the figure.The centre of gravity (CG) of the wing idealized as an airfoil is markedin the figure. The number of degree(s) of freedom for this idealized wing vibrationmodel is _________. (Answer in integer)

explain relation with eigen value and vector.

Mana dari pernyataan berikut yang benar mengenai vektor eigen?Which of the following statements is correct about eigenvectors?ASetiap matriks memiliki vektor eigenEvery matrix has eigenvectorsBSebuah matriks bisa memiliki lebih dari satu vektor eigenA matrix can have more than one eigenvectorCVektor eigen tidak memiliki nilai eigenThe eigen vector does not have eigen valuesDVektor eigen selalu memiliki norma satuThe eigenvector always has a unit norm

Are the eigenvectors of A corresponding to the eigenvalue λ = −1 orthogonal with respect to the usual dot product

Are the eigenvectors of A corresponding to the eigenvalue λ = −1 orthogonal with respect to the usual dot product? If not, apply the Gram-Schmidt process to turn them into an orthonormal set of eigenvectors. A=[3,2,4 2,0,2 4,2,3]