(Solved): 6. For matrix A=202142101. a. Show that 101 ...
![6. For matrix \( A=\left[\begin{array}{ccc}2 & -1 & -1 \\ 0 & 4 & 0 \\ -2 & -2 & 1\end{array}\right] \).
a. Show that \( \lef](https://media.cheggcdn.com/study/44e/44ec90f4-66b9-404c-9f2f-1c80eaf8114c/image)
6. For matrix . a. Show that is an eigenvector of and find the corresponding eigenvalue. (4) b. Show that 4 is an eigenvalue of and find an eigenvector associated with it. (4) c. Show that . (4) d. Is invertible? Briefly explain! e. From the observation that , deduce the value of the third eigenvalue of and find an eigenvector associated with it.
Expert Answer
(a)Characteristic equation (2- ){(4- (1- Thus, the EIGEN VALUE OF MATRIX A are 0,3,4when the corresponding eigen vector is given by -x-y-z=0 .......(1)0.x+y+0.z=0 ..........(2)-2x-2y-2z=0 ......(3)from eqn.(2)y=0put y=0 in eqn.(3)then we get -x-z=0-x=z .....(4)therefore put x=1 in eqn.(4) we get z=-1then the eigen vector= hence proved.