To determine whether the product of two matrices is possible and, if so, to find the dimensions of the resulting matrix, we need to consider the dimensions of the matrices involved.
1. Identify Dimensions of Matrices:
- The first matrix is given as \(\begin{array}{ll}2 & 1\end{array}\), which has dimensions \(1 \times 2\). This means it has 1 row and 2 columns.
- The second matrix is \(\begin{array}{ccc}1 & -1 & 2 \\ -1 & -2 & 1 \\ 0 & 1 & 1\end{array}\), which has dimensions \(3 \times 3\). This means it has 3 rows and 3 columns.
2. Check the Conditions for Matrix Multiplication:
- For matrix multiplication to be possible, the number of columns in the first matrix must equal the number of rows in the second matrix.
- In this case, the first matrix has 2 columns, while the second matrix has 3 rows.
Since the number of columns in the first matrix (2) is not equal to the number of rows in the second matrix (3), matrix multiplication is not possible. Therefore, there is no product, and thus no dimensions for the resulting matrix can be determined.
Conclusion:
Matrix multiplication is not possible with the given matrices.
