Chapter 4: Q17. (page 186)

Find the value of each determinant.
17. $|\begin{matrix} - 7 & 3 \\ - 9 & 7 \end{matrix}|$

Short Answer

Expert verified

The value of the determinant $|\begin{matrix} - 7 & 3 \\ - 9 & 7 \end{matrix}| = - 22$ .

Step by step solution

- Define the determinant of second-order matrix

The determinant of second order matrix is found by calculating the difference of the product of the two diagonals, that is., $|\begin{matrix} a & b \\ c & d \end{matrix}| = a d - b c$ .

- Find the determinant

Apply the definition of the method of finding determinant of second order

matrix $|\begin{matrix} - 7 & 3 \\ - 9 & 7 \end{matrix}|$ .

$|\begin{matrix} - 7 & 3 \\ - 9 & 7 \end{matrix}| = - 7 \times (7) - 3 (- 9)$

- Simplify

To further simplify multiply the values first and then find the difference.

$\begin{matrix} |\begin{matrix} - 7 & 3 \\ - 9 & 7 \end{matrix}| = - 7 \times (7) - 3 (- 9) \\ = - 49 + 27 \\ = - 22 \end{matrix}$

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Find the value of each determinant.
17. $|\begin{matrix} - 7 & 3 \\ - 9 & 7 \end{matrix}|$

Short Answer

Step by step solution

- Define the determinant of second-order matrix

- Find the determinant

- Simplify

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Find the value of each determinant.17.−73−97

Short Answer

Step by step solution

- Define the determinant of second-order matrix

- Find the determinant

- Simplify

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Math Textbooks

Logic and Functions

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Study anywhere. Anytime. Across all devices.

Find the value of each determinant.
17. $|\begin{matrix} - 7 & 3 \\ - 9 & 7 \end{matrix}|$