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

Problem

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

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 element at row 1, column 1 by multiplying the first row of the first matrix by the first column of the second matrix.

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

=3*i2+i

=−3+i

3. Calculate the element at row 1, column 2 by multiplying the first row of the first matrix by the second column of the second matrix.

(i)*(0)+(1+i)*(1+2*i)=0+1+2*i+i+2*i2

=1+3*i−2

=−1+3*i

4. Calculate the element at row 2, column 1 by multiplying the second row of the first matrix by the first column of the second matrix.

(2−3*i)*(2*i)+(4)*(i)=4*i−6*i2+4*i

=8*i+6

=6+8*i

5. Calculate the element at row 2, column 2 by multiplying the second row of the first matrix by the second column of the second matrix.

(2−3*i)*(0)+(4)*(1+2*i)=0+4+8*i

=4+8*i

6. Assemble the resulting matrix using the calculated values.

Final Answer

[[i,1+i],[2−3*i,4]]*[[2*i,0],[i,1+2*i]]=[[−3+i,−1+3*i],[6+8*i,4+8*i]]

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