Chapter 4: Q23. (page 186)

Find the value of each determinant.
23. $|\begin{matrix} 15 & 11 \\ 23 & 19 \end{matrix}|$

Short Answer

Expert verified

The value of the determinant $|\begin{matrix} 15 & 11 \\ 23 & 19 \end{matrix}| = 32$ .

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 $|\begin{matrix} 15 & 11 \\ 23 & 19 \end{matrix}|$ .

$|\begin{matrix} 15 & 11 \\ 23 & 19 \end{matrix}| = 15 \times (19) - (23) (11)$

- Simplify

To further simplify multiply the values first.

$\begin{matrix} |\begin{matrix} 15 & 11 \\ 23 & 19 \end{matrix}| = 15 \times (19) - (23) (11) \\ = 285 - 253 \\ = 32 \end{matrix}$

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Find the value of each determinant.
23. $|\begin{matrix} 15 & 11 \\ 23 & 19 \end{matrix}|$

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.23.15112319

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

Applied Mathematics

Mechanics Maths

Theoretical and Mathematical Physics

Geometry

Pure Maths

Study anywhere. Anytime. Across all devices.

Find the value of each determinant.
23. $|\begin{matrix} 15 & 11 \\ 23 & 19 \end{matrix}|$