Find the Determinant of the Resulting Matrix [[1,-4],[-4,3]][[-11],[5]]

Problem

det([[1,−4],[−4,3]]*[[−11],[5]])

Solution

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

2. Multiply the matrices to find the resulting matrix.

[[1,−4],[−4,3]]*[[−11],[5]]=[[(1)*(−11)+(−4)*(5)],[(−4)*(−11)+(3)*(5)]]

3. Simplify the arithmetic for each entry.

[[−11−20],[44+15]]=[[−31],[59]]

4. Determine if the determinant can be calculated. The resulting matrix is a 2×1 matrix (a vector).

5. Conclude that the determinant is only defined for square matrices (n×n. Since the resulting matrix is 2×1 the determinant is undefined.

Final Answer

det([[1,−4],[−4,3]]*[[−11],[5]])=Undefined

Want more problems? Check here!