Subtract the Matrices [[1,-2,3,-2],[3,1,-1,-5],[2,3,-5,-5]]

Problem

[[1,−2,3,−2],[3,1,−1,−5],[2,3,−5,−5]]−[[(a_11),(a_12),(a_13),(a_14)],[(a_21),(a_22),(a_23),(a_24)],[(a_31),(a_32),(a_33),(a_34)]]

Solution

1. Identify the operation as matrix subtraction. Since only one matrix was provided in the prompt, we assume the task is to represent the general subtraction of two 3×4 matrices or that the second matrix is implied to be zero if not specified. However, usually, "Subtract the Matrices" implies subtracting corresponding elements of two given matrices. If the second matrix is missing, we perform the operation A−B where B is a general matrix of the same dimensions.

2. Subtract corresponding elements from each position (i,j) in the matrices.

3. Calculate the result for the first row:

1−(a_11)

−2−(a_12)

3−(a_13)

−2−(a_14)

4. Calculate the result for the second row:

3−(a_21)

1−(a_22)

−1−(a_23)

−5−(a_24)

5. Calculate the result for the third row:

2−(a_31)

3−(a_32)

−5−(a_33)

−5−(a_34)

Final Answer

[[1,−2,3,−2],[3,1,−1,−5],[2,3,−5,−5]]−[[(a_11),(a_12),(a_13),(a_14)],[(a_21),(a_22),(a_23),(a_24)],[(a_31),(a_32),(a_33),(a_34)]]=[[1−(a_11),−2−(a_12),3−(a_13),−2−(a_14)],[3−(a_21),1−(a_22),−1−(a_23),−5−(a_24)],[2−(a_31),3−(a_32),−5−(a_33),−5−(a_34)]]

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