If $$A=0$$ $$1$$ $$21$$ $$2$$ $$33$$ a $$1$$ and A−$$1=12$$−$$1212$$−$$43c52$$−$$3212$$ , then the values of a and c are respectively is equal to

Question

If $$A=0$$    $$1$$    $$21$$    $$2$$    $$33$$    a    $$1$$ and A−$$1=12$$−$$1212$$−$$43c52$$−$$3212$$ , then the values of a and c are respectively is equal to

Infinity Learn · Accepted Answer

Given that $$A=0121233a1$$ and A−$$1=12$$−$$1212$$−$$43c52$$−$$3212$$ we have $$I=AA$$−$$1=120121233a11$$−$$11$$−$$862c5$$−$$31=120$$−$$8+100+6$$−$$60+2c+21$$−$$16+15$$−$$1+12$$−$$91+4c+33$$−$$8a+5$$−$$3+6a$$−$$33+2ac+1=10c+1012(c+1)4(1$$−$$a)3(a$$−$$1)2+ac$$ Comparing the elements of AA−$$1$$ with those of $$I=1$$    $$0$$    $$00$$    $$1$$    $$00$$    $$0$$    $$1$$ ,  we have $$c+1=0$$ or $$c=$$−$$1a$$−$$1=0$$ or $$a=1$$

$If A = [\begin{array}{lll} 0 1 2 \\ 1 2 3 \\ 3 a 1 \end{array}] and A^{- 1} = [\begin{array}{ccc} \frac{1}{2} & \frac{- 1}{2} & \frac{1}{2} \\ - 4 & 3 & c \\ \frac{5}{2} & \frac{- 3}{2} & \frac{1}{2} \end{array}], then the values of a and c are respectively is equal to$

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If A=0 1 21 2 33 a 1 and A−1=12−1212−43c52−3212 , then the values of a and c are respectively is equal to

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$If A = [\begin{array}{lll} 0 1 2 \\ 1 2 3 \\ 3 a 1 \end{array}] and A^{- 1} = [\begin{array}{ccc} \frac{1}{2} & \frac{- 1}{2} & \frac{1}{2} \\ - 4 & 3 & c \\ \frac{5}{2} & \frac{- 3}{2} & \frac{1}{2} \end{array}], then the values of a and c are respectively is equal to$