Chapter 4: Q7. (page 185)

Find the value of each determinant.
7. $|\begin{matrix} 7 & 8 \\ 3 & - 2 \end{matrix}|$

Short Answer

Expert verified

The value of the determinant $|\begin{matrix} 7 & 8 \\ 3 & - 2 \end{matrix}| = - 38$ .

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 $|\begin{matrix} 7 & 8 \\ 3 & - 2 \end{matrix}|$ .

|\begin{matrix} 7 & 8 \\ 3 & - 2 \end{matrix}| = 7 \times (- 2) - 8 (3)

- Simplify

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

$\begin{matrix} | \begin{matrix} 7 & 8 \\ 3 & - 2 \end{matrix} | = 7 \times (- 2) - 8 (3) \\ = - 14 - 24 \\ = - 38 \end{matrix}$

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Find the value of each determinant.
7. $|\begin{matrix} 7 & 8 \\ 3 & - 2 \end{matrix}|$

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.7.783-2

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

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Study anywhere. Anytime. Across all devices.

Find the value of each determinant.
7. $|\begin{matrix} 7 & 8 \\ 3 & - 2 \end{matrix}|$