Find the Determinant of the Resulting Matrix [[5.50],[6.00]]*[[94,81],[68,89]]

Problem

[[5.50],[6.00]]*[[94,81],[68,89]]

Solution

1. Identify the dimensions of the matrices to determine if the operation is valid. The first matrix is a 2×1 matrix and the second is a 2×2 matrix.

2. Check for matrix multiplication compatibility. For the product A*B to exist, the number of columns in A must equal the number of rows in B

3. Determine the status of the operation. Since the first matrix has 1 column and the second matrix has 2 rows, 1≠2

4. Conclude that the matrix multiplication is undefined. Because the product cannot be formed, a resulting matrix does not exist.

5. Evaluate the determinant requirement. A determinant can only be calculated for square matrices; since the multiplication is impossible, there is no matrix for which to find a determinant.

Final Answer

The product and its determinant are undefined.

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