Simplify the Matrix 3[[1,2],[-2,1]]-4[[-4],[4]]

Problem

3*[[1,2],[−2,1]]−4*[[−4],[4]]

Solution

1. Identify the dimensions of the matrices. The first matrix is a 2×2 matrix, while the second matrix is a 2×1 column vector.

2. Determine if the operation is possible. Matrix subtraction is only defined for matrices of the same dimensions.

3. Conclude that because a 2×2 matrix and a 2×1 matrix have different dimensions, they cannot be subtracted.

Final Answer

3*[[1,2],[−2,1]]−4*[[−4],[4]]=Undefined (Dimension Mismatch)

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