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The characteristic roots of $\begin{bmatrix} 3 &7 \\ 2&5 \end{bmatrix}$ are $\lambda _{1}$ and $\lambda _{2}$, the characteristic roots of $\begin{bmatrix} 5 &-7 \\ -2&3 \end{bmatrix}$ are

  1. $\lambda _{1}$ and $\lambda _{2}$
  2. $2\lambda _{1}$ and $\lambda _{2}$
  3. $\frac{1}{\lambda _{1}}$ and $\frac{1}{\lambda _{2}}$
  4. $\lambda _{1}$ and $2\lambda _{2}$
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If you see both the matrices are inverse of each other and we have given latent roots meaning eigen values of one matrix  are lamda1 and lamda2 so when you do inverse of a matrix according to properties of eigen values ,the eigen value of inverted matrix will get inverted so the answer is  1/lamda1 and 1/lamda2 so answer is c
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