Find the Determinant of the Resulting Matrix

Problem

det([[3*x+y,x−2*y,3*x],[3*x,4*y,x+y]]+[[3*x,8*y,3*x+y],[5*x+2*y,x,3*x]])

Solution

1. Perform matrix addition by adding the corresponding elements of the two 2×3 matrices.

[[(3*x+y)+3*x,(x−2*y)+8*y,3*x+(3*x+y)],[3*x+(5*x+2*y),4*y+x,(x+y)+3*x]]

2. Simplify the terms inside the resulting matrix.

[[6*x+y,x+6*y,6*x+y],[8*x+2*y,x+4*y,4*x+y]]

3. Identify the dimensions of the resulting matrix. The sum of two 2×3 matrices is a 2×3 matrix.

4. Determine the existence of the determinant. The determinant is a property defined only for square matrices (where the number of rows equals the number of columns).

5. Conclude that because the resulting matrix is 2×3 and not square, the determinant is undefined.

Final Answer

det(6*x+y)=Undefined

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