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You are asked to determine the determinant of a 3x3 matrix \( A \):

\[
A = \begin{pmatrix}
-2 & 5 & -3 \\
-1 & -7 & 4 \\
0 & 8 & 6
\end{pmatrix}
\]

The determinant of a 3x3 matrix \( A \) is given by the formula:

\[
\text{det}(A) = a(ei - fh) - b(di - fg) + c(dh - eg)
\]

Where the matrix is:

\[
\begin{pmatrix}
a & b & c \\
d & e & f \\
g & h & i
\end{pmatrix}
\]

Now, using the values from matrix \( A \):
\[
a = -2, \, b = 5, \, c = -3
\]
\[
d = -1, \, e = -7, \, f = 4
\]
\[
g = 0, \, h = 8, \, i = 6
\]

Substituting these values into the formula, let's calculate the determinant.The determinant of the matrix \( A \) is:

\[
\text{det}(A) = 202
\]

Do you have any questions or would you like further details? 

Here are five related questions to expand your understanding:
1. How is the determinant of a 3x3 matrix used in solving linear systems?
2. What does it mean if the determinant of a matrix is zero?
3. How do the cofactor expansion and determinant calculation relate?
4. Can the determinant be applied to matrices larger than 3x3?
5. How does the determinant change if one row or column of the matrix is multiplied by a scalar?

**Tip**: When a determinant is zero, the matrix is singular, meaning it does not have an inverse!

Tentukan determinan matriks ordo 3x3 A = [[-2, 5, -3], [-1, -7, 4], [0, 8, 6]]

Learn how to calculate the determinant of a 3x3 matrix [[-2, 5, -3], [-1, -7, 4], [0, 8, 6]]. This problem explores key concepts in linear algebra, including matrix determinants and the determinant theorem, suitable for students in Grades 10-12.

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