જો B એ 3 times 3 શ્રેણિક છે કે જેથી B^2 | vedclass

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Question

det $\left[ {{{\left( {I + B} \right)}^{50}} - 50B} \right]$

$=$ det $[ {\,^{50}}{C_0}I + {\,^{50}}{C_1}B + {\,^{50}}{C_2}{B^2} + {\,^{50

Vedclass · Accepted Answer

$1$

Vedclass · Answer

det $\left[ {{{\left( {I + B} \right)}^{50}} - 50B} \right]$

$=$ det $[ {\,^{50}}{C_0}I + {\,^{50}}{C_1}B + {\,^{50}}{C_2}{B^2} + {\,^{50}}{C_3}{B^3} + ... +$ $ {\,^{50}}{C_{50}}{B^{50}}{B^{50}} - 50B]$

{All terms having ${B^n},2 \le n \le 50$

will be zero because given that ${B^2} = 0$ }

$=$ det $\left[ {I + 50B - 50B} \right]$$=$ det $[I]=1$

જો $B$ એ $3 \times 3$ શ્રેણિક છે કે જેથી $B^2 = 0$, તો $|( I+ B)^{50} -50B|$ = . . .

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