Question

8.3. In $S_4$, let $\rho = \begin{pmatrix} 1 & 2 & 3 & 4 \ 4 & 1 & 2 & 3 \end{pmatrix}$ and $\tau = \begin{pmatrix} 1 & 2 & 3 & 4 \ 1 & 3 & 2 & 4 \end{pmatrix}$. a) Find $\rho \tau$ and $\tau \rho$. b) Find $\rho^2, \rho^3, \rho^4$. c) Find $\rho^{-1}$ and $\tau^{-1}$.

          8.3. In $S_4$, let
$\rho = \begin{pmatrix} 1 & 2 & 3 & 4 \ 4 & 1 & 2 & 3 \end{pmatrix}$ and $\tau = \begin{pmatrix} 1 & 2 & 3 & 4 \ 1 & 3 & 2 & 4 \end{pmatrix}$.
a) Find $\rho \tau$ and $\tau \rho$.
b) Find $\rho^2, \rho^3, \rho^4$.
c) Find $\rho^{-1}$ and $\tau^{-1}$.

8.3. In S4, let
ρ =
< p m a t r i x > and τ =
< p m a t r i x >.
a) Find ρτ and τρ.
b) Find ρ^2, ρ^3, ρ^4.
c) Find ρ^-1 and τ^-1.

Added by Jessica M.

Calculus: Early Transcendentals

James Stewart 8th Edition

Instant Answer

Solved by Expert Raushan Kumar

05/08/2021

Step 1

This means applying τ first and then ρ. ρτ = ([1,2,3,4],[4,1,2,3]) ∘ ([1,2,3,4],[1,3,2,4]) First, apply τ to the elements: τ([1,2,3,4]) = [1,3,2,4] Now apply ρ to the result: ρ([1,3,2,4]) = [4,1,2,3] Therefore, ρτ = ([1,2,3,4],[4,1,2,3]) Show more…

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In S_(4), let ho =([1,2,3,4],[4,1,2,3]) and au =([1,2,3,4],[1,3,2,4]), a) Find ho au and au ho . b) Find ho ^(2), ho ^(3), ho ^(4). c) Find ho ^(-1) and au ^(-1) 3.3.In S4let a Find pr and T bFind2,3 c Find p-and