Subtract the Matrices

Problem

2*[[1,2],[3,4],[5,6]]−3*[[1,0],[0,4],[7,1]]

Solution

1. Distribute the scalar 2 into the first matrix by multiplying every element by 2

2*[[1,2],[3,4],[5,6]]=[[2*(1),2*(2)],[2*(3),2*(4)],[2*(5),2*(6)]]

[[2*(1),2*(2)],[2*(3),2*(4)],[2*(5),2*(6)]]=[[2,4],[6,8],[10,12]]

2. Distribute the scalar 3 into the second matrix by multiplying every element by 3

3*[[1,0],[0,4],[7,1]]=[[3*(1),3*(0)],[3*(0),3*(4)],[3*(7),3*(1)]]

[[3*(1),3*(0)],[3*(0),3*(4)],[3*(7),3*(1)]]=[[3,0],[0,12],[21,3]]

3. Subtract the corresponding elements of the two resulting matrices.

[[2,4],[6,8],[10,12]]−[[3,0],[0,12],[21,3]]=[[2−3,4−0],[6−0,8−12],[10−21,12−3]]

4. Simplify the arithmetic for each element to find the final matrix.

[[2−3,4−0],[6−0,8−12],[10−21,12−3]]=[[−1,4],[6,−4],[−11,9]]

Final Answer

2*[[1,2],[3,4],[5,6]]−3*[[1,0],[0,4],[7,1]]=[[−1,4],[6,−4],[−11,9]]

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