Answer to Question #152369 in Linear Algebra for Ashweta Padhan

Question

Find the characteristic polynomial of the linear operator T:R^2 tends to R^2 defined by T(a, b)= (3a+5b, 2a-7b)

Answer 1

Find the matrix A that represents T relative to the usual basis of $R^2$ .we have

A= $\begin{bmatrix} 3 & 5 \\ 2 & -7 \end{bmatrix}$

So we look for the trace of A.

tra(A)= 3+(-7) = -4

det(A) = -31

The Characteristics polynomial is.

$t^2-tr(A)t+|A|\\ \implies\\ t^2-(-4)t+(-31)\\ t^2+4t-31\\$