A-matrix-2×2-amp-B-2-3-2-4-such-that-A-T-B-3A-T-5-4-1-1-so-find-det-4A-1-

Question Number 100664 by bobhans last updated on 28/Jun/20

A matrix 2 \times 2 & B = (\begin{matrix} - 2 3 \\ 2 4 \end{matrix}) such that

A^{T} B + {3 A}^{T} = (\begin{matrix} 5 4 \\ - 1 1 \end{matrix}) so find \det ({4 A}^{- 1})

Answered by bramlex last updated on 28/Jun/20

A^{T} (B + 3 I) = (\begin{matrix} 5 4 \\ - 1 1 \end{matrix})

d e t (A^{T}) = d e t (A) = \frac{| \begin{matrix} 5 4 \\ - 1 1 \end{matrix} |}{d e t (B + 3 I)}

= \frac{9}{| \begin{matrix} 1 3 \\ 2 7 \end{matrix} |} = \frac{9}{1} = 9

t h e r e f o r e d e t (4 A^{- 1}) = \frac{16}{d e t (A)} = \frac{16}{9}

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