let-A-1-2-3-3-2-1-M-3-C-1-4-2-1-find-A-1-if-A-inversible-2-calculate-A-n-3-find-cosA-and-sinA-4-is-cos-2-A-sin

Question Number 93418 by abdomathmax last updated on 13/May/20

l e t A = (\begin{matrix} 1 2 3 \\ 3 2 1 \end{matrix}) \in M_{3} (C)

(1 4 2)

1) f i n d A^{- 1} i f A i n v e r s i b l e

2) c a l c u l a t e A^{n}

3) f i n d c o s A a n d s i n A

4) i s {c o s}^{2} A + {s i n}^{2} A = I ?

Commented by abdomathmax last updated on 13/May/20

s o r r y e r r o r o f t y p o A = (\begin{matrix} 1 2 3 \\ 3 2 1 \end{matrix})

(1 3 2)

Commented by i jagooll last updated on 13/May/20

adj (A) = (\begin{matrix} 0 8 - 4 \\ - 5 - 1 8 \\ 10 - 2 - 4 \end{matrix})

\det (A) = 1 (4 - 3) - 2 (4 - 1) + 3 (9 - 2)

= 1 - 6 + 21 = 16

A^{- 1} = \frac{1}{16} adj (A)

= \frac{1}{16} (\begin{matrix} 0 8 - 4 \\ - 5 - 1 8 \\ 10 - 2 - 4 \end{matrix})

Commented by Rio Michael last updated on 13/May/20

sir Jagoll what is the easiest method

to get the Adjucate so far ? please