Given-N-5-3-6-4-and-P-4-3-6-5-find-NP-and-deduce-the-inverse-of-P-

Question Number 57790 by pete last updated on 12/Apr/19

Given N = [\begin{matrix} 5 3 \\ 6 4 \end{matrix}] and P = [\begin{matrix} 4 - 3 \\ - 6 5 \end{matrix}],

find NP and deduce the inverse of P .

Answered by math1967 last updated on 12/Apr/19

[\begin{matrix} 5 & 3 \\ 6 & 4 \end{matrix}] [\begin{matrix} 4 & - 3 \\ - 6 & 5 \end{matrix}] = [\begin{matrix} 20 - 18 & - 15 + 15 \\ 24 - 24 & - 18 + 20 \end{matrix}]

[\begin{matrix} 2 & 0 \\ 0 & 2 \end{matrix}] = 2 I

∴ N P = 2 I \Rightarrow {N P P}^{- 1} = 2 {I P}^{- 1}

\Rightarrow N I = 2 P^{- 1} ∴ 2 P^{- 1} = N

∴ P^{- 1} = [\begin{matrix} 2 & \frac{- 3}{2} \\ - 3 & \frac{5}{2} \end{matrix}]

Commented by pete last updated on 12/Apr/19

Thanks so much

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