Multiply the Matrices [[2i,0],[i,1+2i]]*[[i,1+i],[2-3i,4]]

Problem

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

Solution

1. Identify the rule for matrix multiplication where the element in row i and column j is the dot product of the ith row of the first matrix and the jth column of the second matrix.

2. Calculate the top-left element by multiplying the first row of the first matrix by the first column of the second matrix.

(2*i)*(i)+(0)*(2−3*i)=2*i2+0=−2

3. Calculate the top-right element by multiplying the first row of the first matrix by the second column of the second matrix.

(2*i)*(1+i)+(0)*(4)=2*i+2*i2=2*i−2

4. Calculate the bottom-left element by multiplying the second row of the first matrix by the first column of the second matrix.

(i)*(i)+(1+2*i)*(2−3*i)=i2+(2−3*i+4*i−6*i2)

−1+(2+i+6)=7+i

5. Calculate the bottom-right element by multiplying the second row of the first matrix by the second column of the second matrix.

(i)*(1+i)+(1+2*i)*(4)=i+i2+4+8*i

i−1+4+8*i=3+9*i

6. Assemble the resulting matrix using the calculated values.

Final Answer

[[2*i,0],[i,1+2*i]]*[[i,1+i],[2−3*i,4]]=[[−2,−2+2*i],[7+i,3+9*i]]

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