Matrix multiplication with transpose

Problem

a) \(x={\left( 1,1,-2 \right)}'\) and \(y={\left( 0,1,2 \right)}'\) . Find \(x'x\) , \(x'y\) , \(xx'\) and \(xy'\)

b) \(x={\left( x_1, \ldots ,x_m \right)}'\) and \(y={\left( y_1, \ldots ,y_m \right)}'\) . Find \(x'x\) , \(x'y\) , \(xx'\) and \(xy'\) . Write the first two as a sum.

Solution