Find the Determinant of the Resulting Matrix [[2,7],[-8,-43]][[-6],[9]]

Problem

det(([2,7],[−8,−43])*([−6],[9]))

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 matrix multiplication to find the resulting matrix.

([2,7],[−8,−43])*([−6],[9])=([(2)*(−6)+(7)*(9)],[(−8)*(−6)+(−43)*(9)])

3. Simplify the arithmetic for each entry.

([−12+63],[48−387])=([51],[−339])

4. Determine the determinant of the resulting 2×1 matrix. The determinant is only defined for square matrices (n×n.

5. Conclude that because the resulting matrix is not square, the determinant is undefined.

Final Answer

det(([2,7],[−8,−43])*([−6],[9]))=Undefined

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