Find the Determinant of the Resulting Matrix

Problem

det([[0.95,0.04],[0.05,0.96]]*[[10650000],[650000]])

Solution

1. Identify the dimensions of the matrices. The first matrix is a 2×2 matrix and the second is a 2×1 column vector.

2. Perform the matrix multiplication to find the resulting 2×1 vector.

3. Calculate the first element of the resulting vector:

0.95*(10650000)+0.04*(650000)=10117500+26000=10143500

4. Calculate the second element of the resulting vector:

0.05*(10650000)+0.96*(650000)=532500+624000=1156500

5. Determine the determinant of the resulting 2×1 matrix. By definition, the determinant is only defined for square matrices (n×n.

6. Conclude that because the resulting matrix is a 2×1 matrix and not a square matrix, the determinant does not exist.

Final Answer

det([[0.95,0.04],[0.05,0.96]]*[[10650000],[650000]])=Undefined

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