Question

найти произведения матрицА×Ат и Ат×А: А=(1 2)(3 4)

Answer 1

$A = left[begin{array}{cc}1&2\3&4end{array}right] ; At=left[begin{array}{cc}1&3\2&4end{array}right]$
$A*At=left[begin{array}{cc}1&2\3&4end{array}right] *left[begin{array}{cc}1&3\2&4end{array}right] =left[begin{array}{cc}1*1+2*2&1*3+2*4\3*1+4*2&3*3+4*4end{array}right] =$
$=left[begin{array}{cc}5&11\11&25end{array}right]$
$At*A=left[begin{array}{cc}1&3\2&4end{array}right] *left[begin{array}{cc}1&2\3&4end{array}right] =left[begin{array}{cc}1*1+3*3&1*2+3*4\2*1+4*3&2*2+4*4end{array}right] =$
$=left[begin{array}{cc}10&14\14&20end{array}right]$