If $ A=\left[\begin{array}{cc}5 a & -b \ 3 & 2\end{array}\right] $ and $ A \cdot a d j A=A A^{T} $, then $ 5 a+b $ is equal to

Question

If $ A=\left[\begin{array}{cc}5 a & -b \ 3 & 2\end{array}\right] $ and $ A \cdot a d j A=A A^{T} $, then $ 5 a+b $ is equal to, $ 4 $, $ 13 $, $ -1 $, $ 5 $

MARKS App · Accepted Answer

A = 5 a - b 3 2 and A T = 5 a 3 - b 2 A A T = 25 a 2 + b 2 15 a - 2 b 15 a - 2 b 13 Now, A . a d j A = A I 2 = 10 a + 3 b 0 0 10 a + 3 b Given A A T = A . a d j A 15 a - 2 b = 0 ......(i) 10 a + 3 b = 13 .......(ii) Solving we get 5 a = 2 and b = 3 ∴ 5 a + b = 5

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