https://file.aiquickdraw.com/mathbot/file/1726768031160uw7hotmu.jpg

In the image, we have a 3x3 matrix:

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

It is being added to the expression \( 3(3!) \).

### Step 1: Compute \( 3! \)
The factorial of 3 is:

\[
3! = 3 \times 2 \times 1 = 6
\]

### Step 2: Multiply by 3
Now, multiply \( 3 \times 6 \):

\[
3(3!) = 3 \times 6 = 18
\]

### Step 3: Adding the Scalar to the Matrix
To add a scalar (in this case, 18) to a matrix, typically you add the scalar to each element of the matrix.

So the result of adding 18 to the matrix:

\[
\begin{pmatrix}
3 & 6 & 1 \\
1 & 0 & 4 \\
-4 & 2 & 7
\end{pmatrix}
+ 18
\]

is calculated by adding 18 to each element:

\[
\begin{pmatrix}
3 + 18 & 6 + 18 & 1 + 18 \\
1 + 18 & 0 + 18 & 4 + 18 \\
-4 + 18 & 2 + 18 & 7 + 18
\end{pmatrix}
=
\begin{pmatrix}
21 & 24 & 19 \\
19 & 18 & 22 \\
14 & 20 & 25
\end{pmatrix}
\]

### Final Result:
The final matrix is:

\[
\begin{pmatrix}
21 & 24 & 19 \\
19 & 18 & 22 \\
14 & 20 & 25
\end{pmatrix}
\]

Would you like more details on how matrix operations work or factorial concepts?

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Here are 5 related questions:
1. What is the determinant of the resulting matrix?
2. How does scalar multiplication differ from matrix addition?
3. Can you compute the trace of a matrix? What does it represent?
4. What other matrix operations are commonly used in linear algebra?
5. How do matrix transformations relate to vector spaces?

**Tip**: When adding a scalar to a matrix, ensure it's clear whether you're adding to each element or performing another operation (like scalar multiplication of a matrix).

Solve the matrix addition problem: (3 6 1; 1 0 4; -4 2 7) + 3(3!)

Learn how to add a scalar expression, 3(3!), to a 3x3 matrix. This involves calculating factorials and performing scalar addition. Perfect for students in Grades 9-12, covering key matrix operations and algebra concepts.

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