If $ \mathrm{A}=\left[\begin{array}{lll}0 & 1 & 2 \ 1 & 2 & 3 \ 3 & \mathrm{a} & 1\end{array}\right] \& \mathrm{~A}^{-1}=\left[\begin{array}{lll}1 / 2 & -1 / 2 & 1 / 2 \ -4 & 3 & \mathrm{C} \ 5 / 2 & -3 / 2 & 1 / 2\end{array}\right] $, then values of a \& $ C $ are

Question

If $ \mathrm{A}=\left[\begin{array}{lll}0 & 1 & 2 \ 1 & 2 & 3 \ 3 & \mathrm{a} & 1\end{array}\right] \& \mathrm{~A}^{-1}=\left[\begin{array}{lll}1 / 2 & -1 / 2 & 1 / 2 \ -4 & 3 & \mathrm{C} \ 5 / 2 & -3 / 2 & 1 / 2\end{array}\right] $, then values of a \& $ C $ are, $ -1,1 $, $ 1,2 $, $ 1,-1 $, $ -2,-1 $

MARKS App · Accepted Answer

We have, A = 0 1 2 1 2 3 3 a 1 & A - 1 = 1 / 2 - 1 / 2 1 / 2 - 4 3 C 5 / 2 - 3 / 2 1 / 2 Since, A . A - 1 = I ⇒ A . A - 1 = 0 1 2 1 2 3 3 a 1 1 / 2 - 1 / 2 1 / 2 - 4 3 C 5 / 2 - 3 / 2 1 / 2 = 1 0 C + 1 0 1 2 + 2 C 4 - 4 a 3 a - 3 2 + ac ∴ 1 0 C + 1 0 1 2 + 2 C 4 - 4 a 3 a - 3 2 + ac = 1 0 0 0 1 0 0 0 1 Now, 4 - 4 a = 0 ⇒ a = 1 and C + 1 = 0 ⇒ C = - 1 .

Search any question & find its solution

Looking for more such questions to practice?