Simplify the Matrix

Problem

−2*[[2,−1],[3,4]]+[[2,−1,0],[3,4,1]]*[[2,−1],[3,4],[1,0]]

Solution

1. Perform scalar multiplication on the first matrix by multiplying each entry by −2

−2*[[2,−1],[3,4]]=[[−4,2],[−6,−8]]

2. Multiply the two matrices on the right by calculating the dot product of rows from the first matrix and columns from the second matrix.

[[2,−1,0],[3,4,1]]*[[2,−1],[3,4],[1,0]]=[[(2)*(2)+(−1)*(3)+(0)*(1),(2)*(−1)+(−1)*(4)+(0)*(0)],[(3)*(2)+(4)*(3)+(1)*(1),(3)*(−1)+(4)*(4)+(1)*(0)]]

3. Simplify the entries of the product matrix.

[[4−3+0,−2−4+0],[6+12+1,−3+16+0]]=[[1,−6],[19,13]]

4. Add the resulting matrices together by adding corresponding entries.

[[−4,2],[−6,−8]]+[[1,−6],[19,13]]=[[−4+1,2−6],[−6+19,−8+13]]

5. Calculate the final entries to reach the simplified matrix.

[[−3,−4],[13,5]]

Final Answer

−2*[[2,−1],[3,4]]+[[2,−1,0],[3,4,1]]*[[2,−1],[3,4],[1,0]]=[[−3,−4],[13,5]]

Want more problems? Check here!