Matrix multiplication/C/2-i -1-3i -1 i 0 4-21 times 1+i 1-i 2+5i/Exercise/Solution

Multiplying the first row with the column on the right we get

${}{\begin{aligned}(2-{\mathrm {i} })(1+{\mathrm {i} })+(-1-3{\mathrm {i} })(1-{\mathrm {i} })-(2+5{\mathrm {i} })&=2+2{\mathrm {i} }-{\mathrm {i} }+1-1+{\mathrm {i} }-3{\mathrm {i} }-3-2-5{\mathrm {i} }\\&=-3-6{\mathrm {i} }.\end{aligned}}$

The second row multiplied with the column on the right yields

${}{\mathrm {i} }(1+{\mathrm {i} })+(4-2{\mathrm {i} })(2+5{\mathrm {i} })={\mathrm {i} }-1+8+20{\mathrm {i} }-4{\mathrm {i} }+10=17+17{\mathrm {i} }\,.$

The result is thus the column vector

${\begin{pmatrix}-3-6{\mathrm {i} }\\17+17{\mathrm {i} }\end{pmatrix}}.$

To the exercise