\input cyracc.def
\font\tencyr=wncyr10
\font\tencyrb=wncyb10
\font\tencyri=wncyi10
\font\eightcyr=wncyr8
\input amstex
\def\cyr#1{{\tencyr\cyracc#1}}
\def\cyrb#1{{\tencyrb\cyracc#1}}
\def\cyri#1{{\tencyri\cyracc#1}}
\def\scyr#1{{\eightcyr\cyracc#1}}
\def\N{\bold N}
\def\Q{\bold Q}
\def\R{\bold R}
\def\slikau{\mapsto}
\catcode`@=11
\def\cal#1{{\fam\tw@#1}}
\catcode`@=1

\noindent
\cyrb{4.73} \cyr{(strana 141.) Odrediti matrice slede\'{c}ih linearnih
operatora:}

$\ldots$

{\it 5.} $X\slikau\bmatrix
a&b\cr c&d
\endbmatrix{}X$ \cyr{u prostoru} $\cal M_2(\R)$ \cyr{u kanonichnoj
  bazi jedinichnih matrica;}

$\ldots$

\noindent
\cyrb{Reshenje.} \cyr{Bazu prostora} $\cal M_2(\R)$ \cyr{chine
  matrice}
$$\gather
\bmatrix
1&0\\0&0
\endbmatrix,\quad
\bmatrix
0&1\\0&0
\endbmatrix,\quad
\bmatrix
0&0\\1&0
\endbmatrix,\quad
\bmatrix
0&0\\0&1
\endbmatrix,
\tag{4.2}
\endgather$$
\cyr{chije su slike datim operatorom redom matrice}
$$\hbox{$%
\aligned
\bmatrix
a&b\\c&d
\endbmatrix\bmatrix
1&0\\0&0
\endbmatrix&=\bmatrix
a&0\\c&0
\endbmatrix,\\
\bmatrix
a&b\\c&d
\endbmatrix\bmatrix
0&0\\1&0
\endbmatrix&=\bmatrix
b&0\\d&0
\endbmatrix,
\endaligned$}\qquad\hbox{$%
\aligned
\bmatrix
a&b\\c&d
\endbmatrix\bmatrix
0&1\\0&0
\endbmatrix&=\bmatrix
0&a\\0&c
\endbmatrix,\\
\bmatrix
a&b\\c&d
\endbmatrix\bmatrix
0&0\\0&1
\endbmatrix&=\bmatrix
0&b\\0&d
\endbmatrix.
\endaligned$}$$
\cyr{NJihove koordinate u odnosu na bazu (4.2) su} $(a,0,c,0)$,
$(0,a,0,c)$, $(b,0,d,0)$, $(0,b,0,d)$, \cyr{tj. matrica}
$$\bmatrix
a&0&b&0\\
0&a&0&b\\
c&0&d&0\\
0&c&0&d
\endbmatrix$$
\cyr{je matrica datog operatora.}

\bye