The positive value of the determinant of the matrix A, whose
Adj(Adj(A)) = $$\left( {\matrix{ {14} & {28} & { - 14} \cr { - 14} & {14} & {28} \cr {28} & { - 14} & {14} \cr } } \right)$$, is _____________.
Answer (integer)
14
Solution
<p>$\left| {adj(adj(A))} \right| = {\left| A \right|^{{2^2}}} = {\left| A \right|^4}$</p>
<p>$\therefore$ $${\left| A \right|^4} = \left| {\matrix{
{14} & {28} & { - 14} \cr
{ - 14} & {14} & {28} \cr
{28} & { - 14} & {14} \cr
} } \right|$$</p>
<p>$$ = {(14)^3}\left| {\matrix{
1 & 2 & { - 1} \cr
{ - 1} & 1 & 2 \cr
2 & { - 1} & 1 \cr
} } \right|$$</p>
<p>$= {(14)^3}(3 - 2( - 5) - 1( - 1))$</p>
<p>${\left| A \right|^4} = {(14)^4} \Rightarrow \left| A \right| = 14$</p>
About this question
Subject: Mathematics · Chapter: Matrices and Determinants · Topic: Types of Matrices and Operations
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