Subjects linear algebra

Matrix Product

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Matrix Product


1. **State the problem:** We are asked to find the product of two matrices: Matrix A (1x4): $$\begin{bmatrix}-3 & -4 & 1 & 3\end{bmatrix}$$ Matrix B (2x4): $$\begin{bmatrix}5 & 2 & 0 & -2\\ \end{bmatrix}$$ 2. **Check matrix dimensions for multiplication:** Matrix A is 1 row by 4 columns (1x4). Matrix B is 2 rows by 4 columns (2x4). For matrix multiplication $$A \times B$$ to be defined, the number of columns in A must equal the number of rows in B. Here, A has 4 columns, B has 2 rows, so 4 \neq 2. 3. **Conclusion:** The product $$A \times B$$ is **undefined** because the number of columns in the first matrix (4) does not equal the number of rows in the second matrix (2).