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Chapter 4: Q44. (page 194)

Find the value of each determinant.
44.
$|\begin{matrix} - 5 & 2 \\ 4 & 9 \end{matrix}|$

Short Answer

Expert verified

The value of the given determinant is $- 53$ .

Step by step solution

01

- Description of step.

The value of a second-order determinant can be found out by calculating difference of product of two diagonals.

$|\begin{matrix} a & b \\ c & d \end{matrix}| = a d 鈭� b c$

02

- Find the value of the determinant.

The value of the determinant $|\begin{matrix} 鈭� 5 & 2 \\ 4 & 9 \end{matrix}|$ is given by:

$\begin{matrix} |\begin{matrix} 鈭� 5 & 2 \\ 4 & 9 \end{matrix}| = (鈭� 5) (9) 鈭� (4) (2) \\ = 鈭� 45 鈭� 8 \\ = 鈭� 53 \end{matrix}$

03

- Description of step.

The value of the given determinant is $- 53$ .

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