Find the Determinant of the Resulting Matrix [[-4,0],[3,0]]*[[V],[V^2]]

Problem

det([[−4,0],[3,0]]*[[V],[V2]])

Solution

1. Perform matrix multiplication to find the resulting matrix.

[[−4,0],[3,0]]*[[V],[V2]]=[[(−4)*(V)+(0)*(V2)],[(3)*(V)+(0)*(V2)]]

2. Simplify the entries of the resulting vector.

[[−4*V],[3*V]]

3. Identify the dimensions of the resulting matrix.
   The result is a 2×1 matrix (a column vector).

4. Apply the definition of a determinant.
   The determinant is only defined for square matrices (n×n. Since the resulting matrix is 2×1 it is not a square matrix.

Final Answer

det([[−4,0],[3,0]]*[[V],[V2]])=Undefined (not a square matrix)

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