Find the Determinant of the Resulting Matrix [[2,-1],[4,5]][[3],[7]]

Problem

det([[2,−1],[4,5]]*[[3],[7]])

Solution

1. Multiply the 2×2 matrix by the 2×1 column vector to find the resulting matrix.

[[2,−1],[4,5]]*[[3],[7]]=[[(2)*(3)+(−1)*(7)],[(4)*(3)+(5)*(7)]]

2. Simplify the arithmetic for each entry in the resulting vector.

[[6−7],[12+35]]=[[−1],[47]]

3. Identify that the resulting matrix is a 2×1 matrix (a vector), not a square matrix.

4. Apply the definition of the determinant, which is only defined for square matrices (n×n. Since the result is a 2×1 matrix, the determinant is undefined.

Final Answer

det([[2,−1],[4,5]]*[[3],[7]])=Undefined (not a square matrix)

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