If-A-cos-x-sin-x-sin-x-cos-x-and-A-adj-A-k-1-0-0-1-then-the-value-of-k-is-

Question Number 42728 by RANGAM kumar last updated on 01/Sep/18

If A = [\begin{matrix} \cos x & \sin x \\ - \sin x & \cos x \end{matrix}] and

A adj A = k [\begin{matrix} 1 & 0 \\ 0 & 1 \end{matrix}], then the value of k is

Answered by math1967 last updated on 01/Sep/18

a d j A = {[\begin{matrix} c o s x & s i n x \\ - s i n x & c o s x \end{matrix}]}^{t} = [\begin{matrix} c o s x & - s i n x \\ s i n x & c o s x \end{matrix}]

∴ [\begin{matrix} c o s x & s i n x \\ - s i n x & c o s x \end{matrix}] [\begin{matrix} c o s x & - s i n x \\ s i n x & c o s x \end{matrix}]

[\begin{matrix} {c o s}^{2} x + {s i n}^{2} x & 0 \\ 0 & {s i n}^{2} x + {c o s}^{2} x \end{matrix}]

[\begin{matrix} 1 & 0 \\ 0 & 1 \end{matrix}] = 1 . [\begin{matrix} 1 & 0 \\ 0 & 1 \end{matrix}] ∴ k = 1

Answered by RANGAM kumar last updated on 02/Sep/18

zza

Commented by math1967 last updated on 02/Sep/18

? ? ? ? ? ? w h a t i s w r o n g ?