The matrix provided is:

\[
\begin{pmatrix}
2x & -1 \\
-6 & x - 3
\end{pmatrix}
\]

To find the **determinant** of this \(2 \times 2\) matrix, we use the formula:

\[
\text{determinant} = (a \cdot d) - (b \cdot c)
\]

where the matrix is of the form:

\[
\begin{pmatrix}
a & b \\
c & d
\end{pmatrix}
\]

In your case, \( a = 2x \), \( b = -1 \), \( c = -6 \), and \( d = x - 3 \).

Now calculate the determinant:

\[
\text{determinant} = (2x \cdot (x - 3)) - (-1 \cdot -6)
\]

\[
= (2x^2 - 6x) - 6
\]

\[
= 2x^2 - 6x - 6
\]

Thus, the determinant of the matrix is:

\[
\boxed{2x^2 - 6x - 6}
\]

Would you like more details or have any questions?

### Related Questions:
1. What are the properties of determinants in larger matrices?
2. How does the determinant help in solving systems of equations?
3. Can you find the determinant when \(x = 2\)?
4. How would the determinant change if the second row was \( (-6, 2x - 1) \)?
5. What is the meaning of the determinant being zero?

### Tip:
A matrix with a zero determinant is **singular**, meaning it does not have an inverse.

Learn how to calculate the determinant of the 2x2 matrix (2x -1/ -6 x-3) with a step-by-step solution. This covers the determinant formula for a 2x2 matrix and key matrix algebra concepts. Suitable for high school students in Grades 10-12.

Math Problem Statement

Solution

Ask a new question for Free

By Image

Math Problem Analysis

Mathematical Concepts

Formulas

Theorems

Suitable Grade Level

Related Recommendation