Find the adjoint of the following matrice:Verify that (adjA)A = |A| I = A(adjA) for the above matrice.

Engineering

Mathematics

Introduction to Determinants

Question

Find the adjoint of the following matrice:
$[\begin{array}{cc} - 3 & 5 \\ 2 & 4 \end{array}]$
Verify that (adjA)A = |A| I = A(adjA) for the above matrice.

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

$AdjA = [\begin{array}{cc} + 4 & - 5 \\ - 2 & - 3 \end{array}] = [\begin{array}{cc} 4 & - 5 \\ - 2 & - 3 \end{array}]$

A = [\begin{array}{cc} - 3 & 5 \\ 2 & 4 \end{array}] \Rightarrow detA = - 12 - 10 = - 22

(Adj . A) A = [\begin{array}{cc} + 4 & - 5 \\ - 2 & - 3 \end{array}] [\begin{array}{cc} - 3 & 5 \\ 2 & 4 \end{array}] = [\begin{array}{cc} - 22 & 0 \\ 0 & - 22 \end{array}]

= - 22 [\begin{array}{cc} 1 & 0 \\ 0 & 1 \end{array}]

= |A| I

A . (adjA) = [\begin{array}{cc} - 3 & 5 \\ 2 & 4 \end{array}] = [\begin{array}{cc} 4 & - 5 \\ - 2 & - 3 \end{array}] = [\begin{array}{cc} - 22 & 0 \\ 0 & - 22 \end{array}]

= - 22 [\begin{array}{cc} 1 & 0 \\ 0 & 1 \end{array}]

= |A| I

Please subscribe our Youtube channel to unlock this solution.