Find the Determinant of the Resulting Matrix

Problem

[[26.6,3100,1],[30.2,6400,1],[162,23619,1]]*[[240],[340],[1566]]

Solution

1. Identify the dimensions of the matrices to determine if the operation is valid. The first matrix is 3×3 and the second is 3×1

2. Multiply the matrices to find the resulting vector. The product of a 3×3 matrix and a 3×1 matrix is a 3×1 matrix (a column vector).

3. Calculate the first element of the resulting vector:

(26.6×240)+(3100×340)+(1×1566)=6384+1054000+1566=1061950

4. Calculate the second element of the resulting vector:

(30.2×240)+(6400×340)+(1×1566)=7248+2176000+1566=2184814

5. Calculate the third element of the resulting vector:

(162×240)+(23619×340)+(1×1566)=38880+8030460+1566=8070906

6. Determine the determinant of the resulting matrix. The resulting matrix is a 3×1 matrix.

7. Conclude that the determinant is only defined for square matrices (n×n. Since the resulting matrix is 3×1 it is not square.

Final Answer

The determinant is undefined because the resulting matrix is not square.

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