Question : Verify Cayley Hamilton theorem for the following matrix \[A=\left(\begin{matrix}1&-1&1\\2&-1&0\\1&0&0\end{matrix}\right) \] Solution : Let \[A=\left(\begin{matrix}1&-1&1\\2&-1&0\\1&0&0\end{matrix}\right)\] Then Characteristics equation of A is \[\left|A-xI\right|=0\] \[\left|\begin{matrix}1-x&-1&1\\2&-1-x&0\\1&0&-x\end{matrix}\right|=0\] \[\left(1-x\right)\left(-x\left(-1-x\right)-0\right)-\left(-1\right)\left(-2x-0\right)+1\left(-\left(-1-x\right)\right)=0\] \[x-x^3-2x+1+x=0\] \[x^3-1=0 \] In order to verify Caley Hamilton theorem for the matrix A we…
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