Find the characteristic equation of the given matrix.
-$$A = \left[ \begin{array} { r r r r }
9 & 6 & 4 & 3 \
0 & 7 & - 6 & 8 \
0 & 0 & 5 & 9 \
0 & 0 & 0 & 9
\end{array} \right]$$
A) $( 9 - \lambda ) ^ { 2 } ( 7 - \lambda ) ( 5 - \lambda ) = 0$
B) $( 9 - \lambda ) ( 6 - \lambda ) ( 4 - \lambda ) ( 3 - \lambda ) = 0$
C) $( 9 - \lambda ) ( 7 - \lambda ) ( 5 - \lambda ) = 0$
D) $( 9 - \lambda ) ( 9 - \lambda ) ( 8 - \lambda ) ( 3 - \lambda ) = 0$

Question

Find the characteristic equation of the given matrix.
-$$A = \left[ \begin{array} { r r r r } 
9 & 6 & 4 & 3 \
0 & 7 & - 6 & 8 \
0 & 0 & 5 & 9 \
0 & 0 & 0 & 9
\end{array} \right]$$
A) $( 9 - \lambda ) ^ { 2 } ( 7 - \lambda ) ( 5 - \lambda ) = 0$
B) $( 9 - \lambda ) ( 6 - \lambda ) ( 4 - \lambda ) ( 3 - \lambda ) = 0$
C) $( 9 - \lambda ) ( 7 - \lambda ) ( 5 - \lambda ) = 0$
D) $( 9 - \lambda ) ( 9 - \lambda ) ( 8 - \lambda ) ( 3 - \lambda ) = 0$

Quizplus · Accepted Answer

The characteristic equation of a matrix is found by taking the determinant of $A - \lambda I$, where $I$ is the identity matrix and $\lambda$ is a scalar. For a triangular matrix (including diagonal matrices), the determinant is the product of the diagonal elements minus $\lambda$. Thus, the characteristic equation of the given matrix is $(9-\lambda)^2(7-\lambda)(5-\lambda)=0$, as the diagonal elements are 9, 7, 5, and 9.

Find the Characteristic Equation of the Given Matrix A=[964307−6800590009]A = \left[ \begin{array} { r r r r } 9 & 6 & 4 & 3 \\0 & 7 & - 6 & 8 \\0 & 0 & 5 & 9 \\0 & 0 & 0 & 9\end{array} \right]A=​9000​6700​4−650​3899​​

Find the Characteristic Equation of the Given Matrix $A = \left[ \begin{array} { r r r r } 9 & 6 & 4 & 3 \\0 & 7 & - 6 & 8 \\0 & 0 & 5 & 9 \\0 & 0 & 0 & 9\end{array} \right]$