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Introduction to matrices

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Question

If $[\begin{array}{cc} 2 α + 1 & 3 β \\ 0 & β^{2} - 5 β \end{array}] = [\begin{array}{cc} α + 3 & β^{2} + 2 \\ 0 & - 6 \end{array}]$ find the value of $α$ + $β$

Moderate

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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If $[\begin{array}{cc} x + 3 & 2 y + x \\ z - 1 & 4 w - 8 \end{array}] = [\begin{array}{cc} - x - 1 & 0 \\ 3 & 2 w \end{array}]$ then find the value of $| x + y | + | z + w |$

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