https://file.aiquickdraw.com/mathbot/file/1727366677857y8vntcim.jpg

The problem in the image asks for the determinant of a given matrix. The matrix \( Z \) appears to be a 4x4 matrix, and it is given as follows:

\[
Z = \begin{pmatrix}
6 & -3 & 0 & 9 \\
-1 & 6 & 9 & 1 \\
0 & 10 & 0 & 0 \\
9 & 0 & 0 & 0
\end{pmatrix}
\]

To find the determinant of a 4x4 matrix, we can apply cofactor expansion (Laplace expansion), usually along the first row or column to simplify the calculation. I'll calculate this determinant step by step.

Let me proceed with this calculation.The determinant of the matrix \( Z \) is approximately 7290.

Would you like further details or have any questions about the process? 

Here are some follow-up questions you might find interesting:

1. How is cofactor expansion used to calculate a determinant?
2. What happens if a matrix's determinant is zero?
3. Can determinants help in solving systems of linear equations?
4. How does the determinant relate to matrix invertibility?
5. What are some properties of determinants in larger matrices?

**Tip:** When calculating determinants for larger matrices, it’s often helpful to reduce the matrix size using row or column operations that simplify the computation!

Find the determinant of the following matrix: Z = [[6, -3, 0, 9], [-1, 6, 9, 1], [0, 10, 0, 0], [9, 0, 0, 0]].

Learn how to calculate the determinant of a 4x4 matrix using cofactor expansion. The matrix Z = [[6, -3, 0, 9], [-1, 6, 9, 1], [0, 10, 0, 0], [9, 0, 0, 0]] is solved step by step using linear algebra techniques. Suitable for undergraduate students studying linear algebra.

Math Problem Statement

Solution

Ask a new question for Free

By Image

Math Problem Analysis

Mathematical Concepts

Formulas

Theorems

Suitable Grade Level

Related Recommendation