If , then |adj(adj.A)| =

Engineering

Mathematics

Introduction to Determinants

Question

If $A = [\begin{array}{ccc} 1 & 2 & - 1 \\ - 1 & 2 & 2 \\ 2 & - 1 & 1 \end{array}]$ , then |adj(adj.A)| =

(17)¹

(17)²

(17)³

(17)⁴

LiveFree JEE Main Previous Year Online Papers Live Free JEE Advance Previous Year Online Papers

College PredictorLive

Know your College Admission Chances Based on your Rank/Percentile, Category and Home State.

Get your JEE Main Personalised Report with Top Predicted Colleges in JoSA

Given : $A = [\begin{array}{ccr} 1 & 2 & - 1 \\ - 1 & 2 & 2 \\ 2 & - 1 & 1 \end{array}]$

we know that

det(adj(A)) = |A|^n–1

So, det(adj(adj(A))) = $| A |^{(n - 1)^{2}}$

Now, $| A | = |\begin{array}{ccc} 1 & 2 & - 1 \\ - 1 & 2 & 2 \\ 2 & - 1 & 1 \end{array}|$

$| A | = 1 |\begin{array}{cc} 2 & 2 \\ - 1 & 1 \end{array}| - 2 |\begin{array}{cc} - 1 & 2 \\ 2 & 1 \end{array}| - 1 |\begin{array}{cc} - 1 & 2 \\ 2 & - 1 \end{array}|$

= 1(4) – 2(– 5) – 1(– 3) = 4 + 10 + 3 = 17

and (n – 1)² = (3 –1)² = 2² = 4

∴ det⁡(adj⁡(adj⁡(A))) = (17)⁴

Hence, |adj⁡(adj⁡(A))| = (17)⁴

Please subscribe our Youtube channel to unlock this solution.