Add

Problem

2*[[1,−3,0],[4,5,1],[3,8,0]]*[[1,1,−2],[3,0,4],[−1,3,2]]+[[2,0,−2],[4,7,−5],[1,0,−1]]*[[2,0,−2],[4,7,−5],[1,0,−1]]

Solution

1. Multiply the first two matrices.

[[1,−3,0],[4,5,1],[3,8,0]]*[[1,1,−2],[3,0,4],[−1,3,2]]=[[(1−9+0),(1+0+0),(−2−12+0)],[(4+15−1),(4+0+3),(−8+20+2)],[(3+24+0),(3+0+0),(−6+32+0)]]

[[1,−3,0],[4,5,1],[3,8,0]]*[[1,1,−2],[3,0,4],[−1,3,2]]=[[−8,1,−14],[18,7,14],[27,3,26]]

2. Scale the resulting matrix by 2.

2*[[−8,1,−14],[18,7,14],[27,3,26]]=[[−16,2,−28],[36,14,28],[54,6,52]]

3. Square the third matrix (multiply it by itself).

[[2,0,−2],[4,7,−5],[1,0,−1]]*[[2,0,−2],[4,7,−5],[1,0,−1]]=[[(4+0−2),(0+0+0),(−4+0+2)],[(8+28−5),(0+49+0),(−8−35+5)],[(2+0−1),(0+0+0),(−2+0+1)]]

[[2,0,−2],[4,7,−5],[1,0,−1]]*[[2,0,−2],[4,7,−5],[1,0,−1]]=[[2,0,−2],[31,49,−38],[1,0,−1]]

4. Add the two resulting matrices together.

[[−16,2,−28],[36,14,28],[54,6,52]]+[[2,0,−2],[31,49,−38],[1,0,−1]]=[[(−16+2),(2+0),(−28−2)],[(36+31),(14+49),(28−38)],[(54+1),(6+0),(52−1)]]

[[−16,2,−28],[36,14,28],[54,6,52]]+[[2,0,−2],[31,49,−38],[1,0,−1]]=[[−14,2,−30],[67,63,−10],[55,6,51]]

Final Answer

2*[[1,−3,0],[4,5,1],[3,8,0]]*[[1,1,−2],[3,0,4],[−1,3,2]]+[[2,0,−2],[4,7,−5],[1,0,−1]]2=[[−14,2,−30],[67,63,−10],[55,6,51]]

Want more problems? Check here!