Math Problem Statement

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

Solution

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

\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**.

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Math Problem Analysis

Mathematical Concepts

Matrix Multiplication
Matrix Dimensions

Formulas

Matrix product: (AB)_ij = Σ(A_ik * B_kj)

Theorems

Matrix Multiplication Rule
Dimension Consistency Rule

Suitable Grade Level

Grades 9-12

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