First slide

Applications of determinant

Question

Suppose $A = {(a_{i j})}_{3 \times 3},$ where $a_{i j} \in R$ If $\det (adj A) = 25$ then $| d e t (A) |$ equals:

Moderate

A

5
B

12.5
C

$5 \sqrt{5}$
D

$5^{2 / 3}$

Solution

Using $\det (adj A) = (\det (A))^{2}$ we get
$(\det (A))^{2} = 25 \Rightarrow | \det (A) | = 5$

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