Linear transformation of vector ARMA processes

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Can someone help me to solve the following problem.

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Referring to the one above the bottom equation:

I was managed to get the left hand side and first term of the right hand side. But couldn't solve the remainder to be $(1+0.591B)v_{t}$ and $\sigma^{2}_{v}=2.03$.

Any insight regarding this matter is very helpful.

Thanks.