First slide

Applications of determinant

Question

$If A = [\begin{array}{lll} 3 - 3 4 \\ 2 - 3 4 \\ 0 - 1 1 \end{array}], then the value of trace of the matrix adj (adj A) is$

Moderate

A

1
B

2
C

4
D

16

Solution

$\begin{array}{l} Given matrix A = [\begin{array}{ccc} 3 & - 3 & 4 \\ 2 & - 3 & 4 \\ 0 & - 1 & 1 \end{array}] \\ | A | = 3 (- 3 + 4) + 3 (2 - 0) + 4 (- 2 + 0) \\ = 3 + 6 - 8 \\ = 1 \\ Now, adj (adj (A)) = | A |^{n - 2} A \\ = 1 . A \end{array}$
$\begin{array}{l} = A \\ Trace of the matrix adj (adj A) = 3 - 3 + 1 = 1 \end{array}$

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