Math Problem Statement

Find the determinant of the matrix open square bracket, begin matrix, begin row 1, column 1, 2, column 2, 4, begin row 2, column 1, 1, column 2, 2, end matrix, close square bracket, .[21​42​].

Solution

To find the determinant of a 2x2 matrix, use the formula:

det(A)=ad−bc\text{det}(A) = ad - bc

For the matrix:

2 & 4 \\ 1 & 2 \end{bmatrix}$$ Here, $$a = 2$$, $$b = 4$$, $$c = 1$$, and $$d = 2$$. Now, calculate the determinant: $$\text{det}(A) = (2)(2) - (4)(1) = 4 - 4 = 0$$ So, the determinant of the matrix is **0**. Would you like more details or have any questions about this solution? Here are some related questions you might find interesting: 1. How do you find the determinant of a 3x3 matrix? 2. What happens if the determinant of a matrix is 0? 3. How does the determinant relate to matrix invertibility? 4. What is the geometric interpretation of the determinant? 5. How can you compute the determinant using cofactor expansion? **Tip**: If you ever need to find the determinant of larger matrices, you can break it down using cofactor expansion or row operations to simplify the process.

Ask a new question for Free

By Image

Drop file here or Click Here to upload

Math Problem Analysis

Mathematical Concepts

Linear Algebra
Matrix Determinants

Formulas

det(A) = ad - bc

Theorems

Cofactor Expansion
Matrix Invertibility

Suitable Grade Level

Grades 9-12

Related Recommendation

Evaluate the Determinant of a 2x2 Matrix with Step-by-Step Solution

How to Calculate the Determinant of a 2×2 Matrix

How to Find and Square the Determinant of a 2x2 Matrix: Example with Solution

Calculate the Determinant of a 2x2 Matrix

Determinant of a 2x2 Matrix: Solving \begin{pmatrix} 1 & 2 \\ 3 & 4 \end{pmatrix}