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Chapter 9: Problem 2

Evaluate the determinant. $$\left|\begin{array}{ll}-8 & 6 \\\\-1 & 2\end{array}\right|$$

Short Answer

Expert verified
The determinant is -10.

Step by step solution

01

Identify the Elements of the Matrix

The given matrix is \(\left|\begin{array}{ll}-8 & 6 \ -1 & 2\end{array}\right|\). Identify the elements: \(a = -8\), \(b = 6\), \(c = -1\), and \(d = 2\).
02

Use the Determinant Formula for a 2x2 Matrix

The determinant of a 2x2 matrix \( \left|\begin{array}{ll}a & b \ c & d \end{array}\right| \) is calculated using the formula: \( \text{det} = ad - bc \).
03

Plug in the Values

Substitute the values into the determinant formula: \( \text{det} = (-8)(2) - (6)(-1) \).
04

Perform the Multiplications

Calculate the products in the formula: \( (-8)(2) = -16 \) and \( (6)(-1) = -6 \).
05

Calculate the Determinant

Combine the results from the multiplications: \( -16 - (-6) = -16 + 6 = -10. \) Therefore, the determinant is \( \boxed{-10}. \)

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Key Concepts

These are the key concepts you need to understand to accurately answer the question.

Linear Algebra
Linear algebra is the branch of mathematics that deals with vectors, vector spaces, and linear mappings. It includes the study of matrices and their properties, like determinants. Linear algebra is widely applied in engineering, physics, computer science, and economics.

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