When-A-1-3-1-8-4-find-the-A-A-1-A-

Question Number 171064 by 119065 last updated on 07/Jun/22

W h e n A^{- 1} = [\begin{matrix} 3 & 1 \\ 8 & 4 \end{matrix}]

f i n d t h e A = ?, ∣ A^{- 1} ∣ \cdot A = ?

Answered by som(math1967) last updated on 07/Jun/22

A d j A^{- 1} = {[\begin{matrix} 4 & - 8 \\ - 1 & 3 \end{matrix}]}^{T} = [\begin{matrix} 4 & - 1 \\ - 8 & 3 \end{matrix}]

∣ A^{- 1} ∣= 12 - 8 = 4

A = \frac{1}{4} [\begin{matrix} 4 & - 1 \\ - 8 & 3 \end{matrix}]

∣ A^{- 1} ∣ A = 4 \times \frac{1}{4} [\begin{matrix} 4 & - 1 \\ - 8 & 3 \end{matrix}] = [\begin{matrix} 4 & - 1 \\ - 8 & 3 \end{matrix}]

Commented by 119065 last updated on 07/Jun/22

n i c e s o l u t i o n

Answered by manxsol last updated on 05/Feb/23

t e o r i a

A^{- 1} = \frac{A d j A}{∣ A ∣} \Rightarrow A = \frac{{A d j A}^{- 1}}{∣ A^{- 1} ∣} = \frac{{({c o f a c t A}^{- 1})}^{T}}{∣ A^{- 1} ∣}

A . ∣ A^{- 1} ∣= {({c o f a c t A}^{- 1})}^{T}

Facebook Tweet Pin