If f - - cos- -sin- 0- sin- cos- 0- 0 0 1 -Find i f -ii f - -f -

#160; (1) f ( ∝) = [cos∝ amp; sin∝ amp; 0 sin∝ #160; amp;cos∝ #160; amp; 0 0 amp; 0 amp; 1 ] #160; ∵cos( ∝) = cos∝ ...

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Addition and Subtraction of a Matrix

If f α =[ c...

Question

If $f (α) = ⎡ ⎢ ⎣ \begin{matrix} cos α & - sin α & 0 sin α & cos α & 0 0 & 0 & 1 \end{matrix} ⎤ ⎥ ⎦$ ,
Find
(i) $f (- α)$
(ii) $f (- α) + f (α)$ .

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Solution

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Similar questions

(α)

⎡ ⎢ ⎢ ⎣ \begin{matrix} cos α & - sin α & 0 sin α & cos α & 0 0 & 0 & 1 \end{matrix} ⎤ ⎥ ⎥ ⎦

α ϵ R

F (α) . F (- α) = I_{3}

[F (α)]^{- 1} = F (- α)

F (α) = ⎡ ⎢ ⎣ \begin{matrix} c o s α & - s i n α & 0 s i n α & c o s α & 0 0 & 0 & 1 \end{matrix} ⎤ ⎥ ⎦

[F (α)]^{- 1} = F (- α)

G (β) = ⎡ ⎢ ⎣ \begin{matrix} c o s β & 0 & s i n β 0 & 1 & 0 - s i n β & 0 & c o s β \end{matrix} ⎤ ⎥ ⎦

[G (β)]^{- 1} = G (- β)

f (α) = ⎡ ⎢ ⎣ \begin{matrix} cos α & - sin α & 0 sin α & cos α & 0 0 & 0 & 1 \end{matrix} ⎤ ⎥ ⎦

f (- α) + f (α)

F (α) = ⎛ ⎜ ⎝ \begin{matrix} cos α & - sin α & 0 sin α & cos α & 0 0 & 0 & 1 \end{matrix} ⎞ ⎟ ⎠

{F (x)}^{- 1} = ?

∣ ∣ ∣ ∣ \begin{matrix} cos α & - sin α & 1 sin α & cos α & 1 c o s (α + β) & - sin (α + β) & 1 \end{matrix} ∣ ∣ ∣ ∣

α

f (α) = λ,

f (α)

α

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