Chapter 4: Q39. (page 186)

Solve for x if $\det [\begin{matrix} 2 & x \\ 5 & - 3 \end{matrix}] = 24$ .

Short Answer

Expert verified

The value of $x = - 6$ .

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 $\det [\begin{matrix} 2 & x \\ 5 & - 3 \end{matrix}]$ .

$\begin{matrix} \det [\begin{matrix} 2 & x \\ 5 & - 3 \end{matrix}] = 24 \\ 2 \times (- 3) - 5 (x) = 24 \end{matrix}$

- Simplify for x

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

$\begin{matrix} 2 \times (- 3) - 5 (x) = 24 \\ - 6 - 5 x = 24 \\ - 6 - 5 x + 6 = 24 + 6 \\ - 5 x = 20 \\ x = - 6 \end{matrix}$

Therefore, $x = - 6$ .

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Solve for x if $\det [\begin{matrix} 2 & x \\ 5 & - 3 \end{matrix}] = 24$ .

Short Answer

Step by step solution

- Define the determinant of second-order matrix

- Find the determinant

- Simplify for x

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Solve for x ifdet2x5−3=24.

Short Answer

Step by step solution

- Define the determinant of second-order matrix

- Find the determinant

- Simplify for x

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Math Textbooks

Calculus

Logic and Functions

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Theoretical and Mathematical Physics

Discrete Mathematics

Study anywhere. Anytime. Across all devices.

Solve for x if $\det [\begin{matrix} 2 & x \\ 5 & - 3 \end{matrix}] = 24$ .