https://file.aiquickdraw.com/mathbot/file/17266233934316dspkkl6.jpg

The image presents a 3x3 matrix \( A \) as follows:

\[
A = \begin{pmatrix}
1 & 2 & 3 \\
4 & 5 & 6 \\
7 & 8 & 9
\end{pmatrix}
\]

The task is to calculate the determinant of matrix \( A \), denoted as \( \text{det}(A) \).

The determinant of a 3x3 matrix:

\[
\text{det}(A) = \begin{vmatrix}
a & b & c \\
d & e & f \\
g & h & i
\end{vmatrix} = a(ei - fh) - b(di - fg) + c(dh - eg)
\]

For the given matrix:

\[
A = \begin{pmatrix}
1 & 2 & 3 \\
4 & 5 & 6 \\
7 & 8 & 9
\end{pmatrix}
\]

Substituting the values into the determinant formula:

\[
\text{det}(A) = 1 \times (5 \times 9 - 6 \times 8) - 2 \times (4 \times 9 - 6 \times 7) + 3 \times (4 \times 8 - 5 \times 7)
\]

Let me calculate that.The determinant of matrix \( A \) is:

\[
\text{det}(A) = 0
\]

This indicates that the matrix is singular, meaning it does not have an inverse.

Would you like any further details on this topic, or do you have any other questions?

Here are five related questions you might find interesting:
1. What are the properties of a singular matrix?
2. How do you compute the determinant for a 2x2 matrix?
3. What does it mean geometrically when the determinant of a matrix is zero?
4. How does the determinant help in solving systems of linear equations?
5. Can we determine if a matrix is invertible using its determinant?

**Tip:** If the determinant of a matrix is zero, this means its rows or columns are linearly dependent.

Jika A = [[1, 2, 3], [4, 5, 6], [7, 8, 9]] maka det(A) adalah?

This solution calculates the determinant of matrix A = [[1, 2, 3], [4, 5, 6], [7, 8, 9]], applying the determinant formula for 3x3 matrices. Discover how the determinant results in 0, indicating a singular matrix. Ideal for students in Grades 9-12 studying linear algebra.

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