1. Tardigrade
  2. Question
  3. Mathematics
  4. if A [1&2 2&1]and f(x) = (1+x) (1 - x), then f(A) is

Question Error Report

Thank you for reporting, we will resolve it shortly

Back to Question

Q. if $A \begin{bmatrix}1&2\\ 2&1\end{bmatrix}$and $f(x) = (1+x) (1 - x)$, then $f(A)$ is

Matrices

Solution:

Given, $f[x) = (1 + x) (1 - x) = 1 - x^2$
$\Rightarrow f(A) = I - A^2 (\because$ Put $x = A$)
$\Rightarrow f\left(A\right) = \begin{bmatrix}1&0\\ 0&1\end{bmatrix}-\left\{\begin{bmatrix}1&2\\ 2&1\end{bmatrix}\begin{bmatrix}1&2\\ 2&1\end{bmatrix}\right\}$
$=\begin{bmatrix}1&0\\ 0&1\end{bmatrix}-\begin{bmatrix}5&4\\ 4&5\end{bmatrix}=\begin{bmatrix}-4&-4\\ -4&-4\end{bmatrix}$
$ = -4 \begin{bmatrix}1&1\\ 1&1\end{bmatrix}$