If 2α+13β0β2−5β=α+3β2+20−6 find the value of α + β

Solution:

The given matrices will be equal, iff

$\begin{array}{l} 2 α + 1 = α + 3 \Rightarrow α = 2 \\ 3 β = β^{2} + 2 \Rightarrow β^{2} - 3 β + 2 = 0 \\ β = 1, 2 and β^{2} - 5 β = - 6 - - - (i) \\ β^{2} - 5 β + 6 = 0 \\ β = 2, 3 - - - - (ii) \end{array}$

From Eqs. (i) and (i), we get $β$ =2

$α = 2, β = 2$

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