If the matrices A = $$\left[ {\matrix{
1 & 1 & 2 \cr
1 & 3 & 4 \cr
1 & { - 1} & 3 \cr
} } \right]$$,
B = adjA and
C = 3A, then ${{\left| {adjB} \right|} \over {\left| C \right|}}$ is equal to :
Solution
A = $$\left[ {\matrix{
1 & 1 & 2 \cr
1 & 3 & 4 \cr
1 & { - 1} & 3 \cr
} } \right]$$
<br><br>$\Rightarrow$ |A| = 6
<br><br>${{\left| {adjB} \right|} \over {\left| C \right|}}$
<br><br>= ${{\left| {adj\left( {adjA} \right)} \right|} \over {\left| {3A} \right|}}$
<br><br>= ${{{{\left| A \right|}^4}} \over {{3^3}\left| A \right|}}$
<br><br>= ${{{{\left| A \right|}^3}} \over {{3^3}}}$
<br><br>= ${{{6^3}} \over {{3^3}}}$ = 8
About this question
Subject: Mathematics · Chapter: Matrices and Determinants · Topic: Types of Matrices and Operations
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