Compute the product. This exercise should be done two ways: by hand and by using technology where possible. (If an answer is undefined, enter UNDEFINED in any cell of the matrix.)

1	0	−1

1	1	2

0	−1	1

−1	0	−1
4	6	0

Let's compute the product of the two matrices by hand and using technology. You have two matrices:

\[
A =
\begin{pmatrix}
1 & 0 & -1 \\
1 & 1 & 2 \\
0 & -1 & 1
\end{pmatrix}
\]
and
\[
B =
\begin{pmatrix}
-1 & 0 & -1 \\
4 & 6 & 0
\end{pmatrix}
\]

### 1. **Matrix Dimensions Check:**
Matrix \( A \) is a \( 3 \times 3 \) matrix, and matrix \( B \) is a \( 2 \times 3 \) matrix.

To multiply matrices \( A \) and \( B \), the number of columns in \( A \) must equal the number of rows in \( B \). However, matrix \( B \) has 2 rows, and matrix \( A \) has 3 columns. Thus, the multiplication is **undefined**.

The product of a \( 3 \times 3 \) matrix and a \( 2 \times 3 \) matrix is not possible.

### Answer:
The product of the matrices is **undefined**.

Compute the product. This exercise should be done two ways: by hand and by using technology where possible. (If an answer is undefined, enter UNDEFINED in any cell of the matrix.)

1	0	−1
1	1	2
0	−1	1

−1	0	−1
4	6	0

Learn how to determine if matrix multiplication is possible between a 3x3 matrix and a 2x3 matrix. This problem explores matrix dimensions, matrix product rules, and when the result is undefined. Suitable for students in Grades 9-12.

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