1 -MATERIAL_ALGA

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!"#$%&'(
 !" !"#$%& '( )$'(! m *)$ n+ ),'( m - ) ,.!($) '( /%,0"1 ( n - ) ,.!($) '( 2)/3,"1+
- 3!" #"4(/" 2)!*)1#" *)$ m× n (/(!(,#)1 ( - $(*$(1(,#"'" '" 1(53%,#( 6)$!"7
A =


a11 a12 a13 . . . a1n
a21 a22 a23 . . . a2n
a31 a32 a33 . . . a3n
8
8
8
8
8
8
8
8
8
8
8
8
8
8
8
am1 am2 am3 . . . amn


),'( 2"'" (/(!(,#) '" !"#$%& *)'( 1($ $(*$(1(,#"') ," 6)$!" aij+ i = 1, ..., m ( j = 1, ..., n8
93#$" $(*$(1(,#":;) *"$" " !"#$%& A "2%!" *)'( 1($ A = [aij]+ i = 1, ..., m ( j = 1, ..., n8
< )$*'+ '( 3!" !"#$%& - '"'" *(/) ,.!($) '( /%,0"1 ( 2)/3,"1 =3( (/" *)113%8
,-'+./) 0 >),1%'($( "1 !"#$%&(1 A+ B+ C+ D+ E ( F 7
A =
( −1 2 1
5 3 0
)
B =
(
1 0 8 −1
2
)
C =

 −35
7


D =


1 5 −3 4
2 1 2 7
5 −2 1 2
0 0 −√2 1

 E =


1 2 3
4 5 6
1 2 3
4 5 6

 F =
(
0 1
2 −1
)
• < !"#$%& A - '" )$'(! 2 *)$ 3 ( *)113% 2 × 3 = 6 (/(!(,#)18 ?1#" !"#$%& #"!4-!
- 20"!"'" '( +"#$%& $'#"123/"$ *)%1 ) ,.!($) '( /%,0"1 - '%6($(,#( ') ,.!($) '(
2)/3,"1@
• < !"#$%& B - '" )$'(! 1 *)$ 4 ( *)113% 1 × 4 = 4 (/(!(,#)18 ?1#" !"#$%&+ *)$ #($
1)!(,#( 3!" /%,0"+ - 20"!"'" '( +"#$%& /%14"8 !" !"#$%& /%,0" #"!4-! - 3!"
!"#$%& $(#",53/"$8
• < !"#$%& C - '" )$'(! 3 *)$ 1 ( *)113% 3 × 1 = 3 (/(!(,#)18 ?1#" !"#$%&+ *)$ #($
1)!(,#( 3!" 2)/3,"+ - 20"!"'" '( +"#$%& 5)/31"8 !" !"#$%& 2)/3," #"!4-! -
3!" !"#$%& $(#",53/"$8
• < !"#$%& D - '" )$'(! 4 *)$ 4 ( *)113% 4× 4 = 16 (/(!(,#)18 ?1#" !"#$%&+ *)$ #($ )
,.!($) '( /%,0"1 %53"/ ") ,.!($) '( 2)/3,"1+ - 20"!"'" '( +"#$%& 63"*$"*"8
• < !"#$%& E - '" )$'(! 4 *)$ 3 ( *)113% 4 × 3 = 12 (/(!(,#)18 ?1#" !"#$%& - 3!"
!"#$%& $(#",53/"$8
• < !"#$%& F - '" )$'(! 2 *)$ 2 ( *)113% 2×2 = 4 (/(!(,#)18 ?1#" !"#$%& - 3!" !"#$%&
=3"'$"'"8
78('$9":;)0 !" !"#$%& 23A)1 (/(!(,#)1 1;) #)')1 ,3/)1 - 20"!"'" '( +"#$%& &'$)8
?/" *)'( 1($ $(*$(1(,#"'" *)$ B0B8
0 =
(
0 0
0 0
)
0 =
(
0 0 0
0 0 0
)
C
 ! "#$%&' ()#*%#*#
 ! "!# !#$%&' ("#)%#)# * +,!-%* )- .&+/#0 1 &2"#. #* +,!-%* )- 3*."+#04 500&! "!#
!#$%&' A )- *%)-! n 6*% n 6*)- 0-% %-6%-0-+$#)#7
A =


a11 a12 . . . a1n
a21 a22 . . . a2n
4
4
4
4
4
4
4
4
4
4
4
4
an1 an2 . . . ann


80 -.-!-+$*0 -! ("- i = j9 3*+0$&$"-! # *&#+,-#. /%&-0&/#.4
A =


a11 a12 . . . a1n
a21 a22 . . . a2n
4
4
4
4
4
4
4
4
4
4
4
4
an1 an2 . . . ann

 =


a11 ∗ . . . ∗
∗ a22 . . . ∗
4
4
4
4
4
4
4
4
4
4
4
4
∗ ∗ . . . ann


80 -.-!-+$*0 -! ("- i + j = n + 19 3*+0$&$"-! # *&#+,-#. 120)-*3%&#4
A =


a11 . . . a1 n−1 a1n
a21 . . . a2 n−1 a2n
4
4
4
4
4
4
4
4
4
4
4
4
an1 . . . an n−1 ann

 =


∗ . . . ∗ a1n
∗ . . . a2 n−1 ∗
4
4
4
4
4
4
4
4
4
4
4
4
an1 . . . ∗ ∗


5 !#$%&' ("#)%#)# ("- 6*00"& *0 -.-!-+$*0 aij = 0 6#%# i 6= j 1 3/#!#)# )- 4#$%&'
*&#+,-#.4
A =


a11 0 . . . 0
0 a22 . . . 0
4
4
4
4
4
4
4
4
4
4
4
4
0 0 . . . ann

 B =


−1 0 0 0
0 0 0 0
0 0 1
4
0
0 0 0 3


5 4#$%&' 210#.#% 1 "!# !#$%&' )&#2*+#. -! ("- *0 -.-!-+$*0 aij9 6#%# i = j9 0:* &2"#&04
A =


k 0 . . . 0
0 k . . . 0
4
4
4
4
4
4
4
4
4
4
4
4
0 0 . . . k

 B =

 −2 0 00 −2 0
0 0 −2


5 4#$%&' &*2-$&*#*2 1 "!# !#$%&' -03#.#% -! ("- aij = 19 6#%# i = j4
;
A =


1 0 . . . 0
0 1 . . . 0
 
 
 
 
 
 
 
 
 
 
 
 
0 0 . . . 1

 B =
(
1 0
0 1
)
C =

 1 0 00 1 0
0 0 1


 !" #$%&'()%* %+,&% -',&./%*
 !"! 012'34'4% 4% -',&./%*
!"#$ %#&'()*$ A = [aij] * B = [bij] +i = 1, ..., m * j = 1, ..., n, -* 5%*5' 6&4%5 $./
(0"#($ $* /$ *1*%*2&/$ 3"* *$&./ 2# %*$%# 4/$(5./ $./ (0"#($6 /" $*7#6 aij = bij 
8/%/ 4/' *9*%41/ $* A =
(
2 3 0
5 1 2
)
* B =
(
2 3 0
5 1 2
)
6 *2&./ A = B 
78%5$36 "9 !#-#$ #$ %#&'()*$ A =
(
y + 4 2
9 x2 + 4
)
* B =
(
12 2
9 53
)
 8#1:"1#' x
* y 4#'# 3"* A * B $*7#% (0"#($ 
 !"!" :4.(;6 % <2=,&'(;6 4% -',&./%*
;*7# A = [aij] * B = [bij] -"#$ %#&'()*$ -* %*$%# /'-*% 
• :4.(;6 4% -',&./%*9 < %#&'() C = [cij]6 /2-* C = A + B6 = # %#&'() *% 3"* /$
*1*%*2&/$ $./ -#-/$ 4/' cij = aij + bij 
• <2=,&'(;6 4% -',&./%*9 < %#&'() E = [eij]6 /2-* E = A−B6 = # %#&'() *% 3"* /$
*1*%*2&/$ $./ -#-/$ 4/' eij = aij − bij 
78%5$36 >9 !#-#$ #$ %#&'()*$
A =

 2 3 8−5 9 −6
7 4 −1

 B =

 −3 7 1−4 2 5
0 9 4

 C =

 7 −8 34 −3 2
9 −5 1


8#1:"1* A + B * C −B 
>
 !"#!$%&'&%() !"#$ A% B% C ! 0 $#&'()!* +! $!*$# ,'+!$-
*+ A + (B + C) = (A + B) + C.
**+ A + 0 = 0 + A = A /0!$1'! 23! #23( , 454 '!6'!*!7&# # $#&'() )!', ! !8# 9 , !8!$!7&,
7!3&', +# #+(:;, +! $#&'()!*<.
***+ −A + A = A− A = 0.
*,+ A + B = B + A=
-./.0 !"&12" &% 13' 4'2!$5 #"! 13 6(7'8'!
 !"# A = [aij] 3$# $#&'() ! *!"# k 3$ !*>#8#' /7?$!', '!#8<= @ $#&'() B = [bij]% ,7+!
B = kA% 9 # $#&'() !$ 23! ,* !8!$!7&,* *;, +#+,* 6,' bij = kaij=
69%3#8" :) A#+# # $#&'() A =

 4 3−2 −5
1 0


= A!&!'$(7! B &#8 23! B = −3A=
69%3#8" ;) !"# A% B ! C +, !B!$68, C= A!&!'$(7! D &#8 23! D = 3A−B + 4C
 !"#!$%&'&%() !"#$ λ ! µ !*>#8#'!* !% A ! B $#&'()!* +! $!*$# ,'+!$-
*+ (λµ)A = λ(µA) .
**+ (λ + µ)A = λA + µA.
***+ λ(A + B) = λA + λB.
*,+ 1A = A=
D
 !"!# $%&'()& '* (+, -,)%./ 0&% 1()%,
 !"! #!$%&%'!"( )!*+, "-."-,-/'!" .+" (m,n) ! +"0-* 0- 1*! *!'"%2 m .+" n3
4+/,%0-"- +, ,-51%/'-, -6-*.&+,7
83 9-:!* !, *!'"%2-, A =
( −1 3 0 4 )
- B =


−6
1
5
1
2


; ."+01'+ AB <( .+" 0-fi/%>?+( ! *!'"%2 C = [c11] '!& @1-7
C11 = (−1)× (−6) + 3× 1 + 0× 5 + 4×
(
1
2
)
= 11
A%2-*+, @1- 11 < + ."+01'+ 0! *!'"%2 B .-&! *!'"%2 C3 +"'!/'+ C = (11).
$,%, 0&'*%+&2 +(3).03.4,% (+, +,)%./ A 0&% (+, +,)%./ B 5 0%*4.2& 6(* &
78+*%& '* 4&3(7,2 '* A 2*9, .:(,3 ,& 78+*%& '* 3.7;,2 '* B! < &%'*+ ',
+,)%./ %*2(3),7)* '*2)* 0%&'()& 5 ',', 0*3& 78+*%& '* 3.7;,2 '* A * 0*3&
78+*%& '* 4&3(7,2 '* B!
D+ -6-*.&+ !$%*! ! +"0-* 0! *!'"%2 A < (1, 4) - 0! *!'"%2 B < (4, 1)3 ;E,-")- @1-
+ /F*-"+ 0- $+&1/!, 0- A < + *-,*+ @1- + /F*-"+ 0- &%/G!, 0- B - @1- ! +"0-* 0!
*!'"%2 C < (1, 1) H1*! &%/G! - 1*! $+&1/! I 1*! *!'"%2 0- 1* -&-*-/'+J3
K3 4+/,%0-"- !, *!'"%2-, A =
(
5 2 3 4
)
- B =


3 4
5 7
4 2
6 1

3 L!*+, 0-'-"*%/!" ! *!I
'"%2 C = AB3
B +"0-* 0! *!'"%2 A < (1, 4) - ! +"0-* 0! *!'"%2 B < (4, 2)3 4+*+ + /F*-"+ 0-
$+&1/!, 0- A < %51!& !+ /F*-"+ 0- &%/G!, 0- B < .+,,M)-& #!2-" ! *1&'%.&%$!>?+ 0- A
.+" B3 B +"0-* 0! *!'"%2 C ,-"N (1, 2)( +1 ,-:!( ,-"N 1*! *!'"%2 0! #+"*!7
C =
(
c11 c12
)
+/0-7
C11 = 5× 3 + 2× 5 + 3× 4 + 4× 6 = 61
C12 = 5× 4 + 2× 7 + 3× 2 + 4× 1 = 44
.+"'!/'+ C =
(
61 44
)
O
 ! "#$%&'()( *% +*,)&-(% A =
(
2 −1 3
5 2 4
)
( B =

 1 2 5 −13 4 7 0
2 3 1 6


! .*+#% '(,()+&/
$*) * +*,)&- C = AB!
0 #)'(+ '* +*,)&- A 1 (2, 3) ( * #)'(+ '* +*,)&- B 1 (3, 4)! "#+# # $2+()# '(
3#45$*% '( A 1 &65*4 *# $2+()# '( 4&$7*% '( B 1 8#%%9:(4 ;*-() * +54,&84&3*<=# '( A
8#) B! 0 #)'(+ '* +*,)&- C %()> (2, 4)? #5 %(@*? %()> 5+* +*,)&- '* ;#)+*A
C =
(
c11 c12 c13 c14
c21 c22 c23 c24
)
#$'(A
c11 = 2× 1 + (−1)× 3 + 3× 2 = 5
c12 = 2× 2 + (−1)× 4 + 3× 3 = 9
c13 = 2× 5 + (−1)× 7 + 3× 1 = 6
c14 = 2× (−1) + (−1)× 0 + 3× 6 = 16
c21 = 5× 1 + 2× 3 + 4× 2 = 19
c22 = 5× 2 + 2× 4 + 4× 3 = 30
c23 = 5× 5 + 2× 7 + 4× 1 = 43
c24 = 5× (−1) + 2× 0 + 4× 6 = 19
8#),*$,# C =
(
5 9 6 16
19 30 43 19
)
B! "#$%&'()( *% +*,)&-(% A ( B '# &,(+ ! C 8#%%9:(4 '(,()+&$*) # 8)#'5,# E = B.ADE=# 1 8#%%9:(4 8#&% 3#+# * #)'(+ '*% +*,)&-(% B 1 (3, 4) ( '* A 1 (2, 3)? ,(+#% F5( #
$2+()# '( 3#45$*% '( B 1 '&;()($,( '# $2+()# '( 4&$7*% '( A!
 !"#$%&'()* +),-.&./%/0&0# 0& 1-2./32/4&'() 0# 5-&" 1&.$/6#"
G5*$'# $#% )(;()&+#% * +*,)&-(%? %( # 8)#'5,# AB (H&%,(? $=# F5() '&-() F5( # 8)#'5,#
BA ,*+I1+ (H&%,*!
J( ,#+*)+#% * +*,)&- A '( #)'(+ (3, 5) ( * +*,)&- B '( #)'(+ (5, 6)? * +54,&84&3*<=#
AB 8#'( %() )(*4&-*'* 8#&% # $2+()# '( 3#45$*% '( A 1 &65*4 *# $2+()# '( 4&$7*% '( B ( *
+*,)&- '(%,( 8)#'5,# %()> 5+* '( #)'(+ (3, 6)! K> * +54,&84&3*<=# BA $=# (%,*)> '(fi$&'*
8#&% # $2+()# '( 3#45$*% '( B $=# 1 &65*4 *# $2+()# '( 4&$7*% '( A!
J( *% +*,)&-(% A ( B ;#)(+ F5*')*'*% '( +(%+* #)'(+ 1 8#%%9:(4 '(,()+&$*) #% 8)#'5,#%
AB ( BA 8#)1+ (4(% $=# %()=# $(3(%%*)&*+($,( &65*&%! J#+($,( ,()(+#% AB = BA %( 5+*
'*% +*,)&-(% ;#) * +*,)&- &'($,&'*'( #5 %( 5+* ;#) * +*,)&- &$:()%* '* #5,)* MF5( :()(+#% *
%(65&)N!
O
 !"#$%& '( !"#$%&'& (# )(*'$+&# A =
(
1 2
5 4
)
, B =
( −1 3
1 5
)
& C =
(
1 0
0 1
)
-
 (./0.& AB, BA, AC & CA-
)*+ ,-./01 234"/5-
1(%(# %0(# )(*'$+&# 20(%'(%(# A & B %& )&#)( !'%&), #&
AB = BA = I !"%& I 3 ( )(*'$+ $%&"*$%(%&
&"*4! %$+&)!# 20& B 3 ( #-./01 034"/5- %& A & 5!%&)!# '&5'&#&"*(' B = A−1 6!0 &"*4!
20& A 3 ( )(*'$+ $"7&'#( %& B & 5!%&)!# '&5'&#&"*(' A = B−18- 9&#*& /(#! ( /!)0*(*$7$%(%&
&"*'& (# )(*'$+&# 3 7:.$%(-
;##$), 5!%&)!# &#/'&7&' AA−1 = A−1A = I-
 !"#$%& 6( 1(%(# (# )(*'$+&#
A =

 −1 −1 00 −1 −1
1 −1 −3


& B =

 −2 3 −11 −3 1
−1 2 −1


7&'$fi20& #& B 3 $"7&'#( %& A-
7/&$/0"8-8"5(
29 1(%(# (# )(*'$+&# A, B & C %& !'%&) (m,n), (n, p) & (p, r), '&#5&/*$7()&"*&, *&)=#&
(AB)C = A(BC)>
229 1(%(# (# )(*'$+&# A, B & C %& !'%&) (m,n), (m,n) & (n, p), '&#5&/*$7()&"*&, *&)=#&
(A + B)C = AC + BC>
2229 1(%(# (# )(*'$+&# A, B & C %& !'%&) (n, p), (n, p) & (m,n), '&#5&/*$7()&"*&, *&)=#&
C(A + B) = CA + CB>
?
 !" ! A(m,n)" #!$%&! ImA = AIn = A'
!" ()*)& )& $)#+,-!& A ! B *! .+*!$ (m,n) ! (n, p)" +!&/!0#,1)$!2#!" #!$%&!" /)+) #.*.
23$!+. λ" 45! (λA)B = A(λB) = λ(AB)'
! " 6 $57#,/7,0)89. $)#+,0,)7 29. :" !$ ;!+)7" 0.$5#)#,1)<
#$%&'() *+ ()*)& )& $)#+,-!& A =
(
9 5
7 4
)
! B =
(
4 n
m 9
)
< =)7057)+ m ! n /)+)
45! B &!>) ,21!+&) *! A<
,-. /01234 52067')710
6 &01234 12067')710 *) $)#+,- 6 *! .+*!$ (m,n)" : ) $)#+,- AT *! .+*!$ (n,m) 45!
&! .?#:$ *) $)#+,- A /!+$5#)2*. )& 7,2@)& /!7)& 0.752)& *! $!&$. A2*,0!<
=.2&,*!+)2*." /.+ !B!$/7." ) $)#+,- A *! .+*!$ (3, 2) *)*) /.+C
A =

 a11 a12a21 a22
a31 a32


!2#9. ) &5) #+)2&/.&#) &!+D ) $)#+,- AT *! .+*!$ (2, 3) *)*) /.+
AT =
(
a11 a21 a31
a12 a22 a32
)
#$%&'() 8+ ()*)& )& $)#+,-!& A =

 1 30 2
2 4


" B =
(
1 2
3 4
)
! C =
(
0 2
−1 3
)
<
(!#!+$,2! (C + B)T " CT + BT " (AB)T ! BT AT <
E
 !"#!$%&'&%()
*+ (A + B)T = AT + BT !"#$ A $ B %&! '()*+,$% #$ '$%'( !*#$'-
**+ (λA)T = λAT .(*( λ $%/(0(*-
***+ (AT )T = A-
*,+ (AB)T = BT AT #$%#$ 12$ ! "3'$*! #$ /!02"(% #$ A %$4( +52(0 (! "3'$*! #$ #$ 0+"6(%
#$ B7
-./ 0'1!$2 3$451!$6'
8'( '()*+, 12(#*(#( A = [aij] 9 #+)( ($451!$6' %$ $0( 9 +52(0 ( %2( )*(%.!%)( !2 %$4( 
A = AT 7
78%4#9" -:) :$*+fi12$ %$ ( '()*+, A =

 1 5 95 3 8
9 8 7


9 %+'9)*+/(7
;<(%!='>?")
• <' 2'( '()*+, %+'9)*+/( !% $0$'$")!% #+%.!%)!% %+'$)*+/('$")$ $' *$0(=&! ( #+(5!"(0
.*+"/+.(0 %&! +52(+% !2 %$4( aij = aji7
• > .*!#2)! #$ 2'( '()*+, @A'&!'&' .$0( %2( )*("%.!%)( 9 2'( '()*+, %+'9)*+/(7
78%4#9" --) ?(#( ( '()*+, A =

 2 0 21 −1 2
0 3 0


7 ?$)$*'+"$ AAT 7
-.B 0'1!$2 CD1$(($451!$6'
8'( '()*+, 12(#*(#( A = [aij] 9 #+)( 'D1$(($451!$6' %$ A
T = −A7
78%4#9" -E) :$*+fi12$ %$ ( '()*+, A =

 0 3 4−3 0 −6
−4 6 0


9 (")+%%+'9)*+/(7
@
 !"#$%&'()* ! "!# !#$%&' #($&))&!*$%&+#, -) ./.!.($-) 0&)1-)$-) )&!.$%&+#!.($. .!
%./#23- # 0&#4-(#/ 1%&(+&1#/ 1-))".! )&(#&) -1-)$-), -" ).5#, aij = −aji . -) ./.!.($-) 0#
0&#4-(#/ 1%&(+&1#/ )3- ("/-)6
+,- .&/$01 $/)2)3&4
7!# !#$%&' M .! 8". # &(9.%)# +-&(+&0. +-! # $%#()1-)$# * 0.(-!&(#0# 5&/$01 )$6
/)2)3&4, -" ).5#:
M−1 = MT ;<=
>"/$&1/&+#(0- # .8"#23- ;<= .! #!?-) -) /#0-) 1-% M :
• MM−1 = MMT ⇒ I = MMT
• M−1M = MT M ⇒ I = MT M
@))&!, MT M = MMT = I6
78#594) +:* >-)$%. 8". # !#$%&' A =
(
1
2
√
3
2√
3
2
−1
2
)
* -%$-4-(#/6
+,; .&/$01#" <$0&32=4&$ >=9#$0)$ # <$0&32=4&$ ?3@#$0)$
7!# !#$%&' <$0&32=4&$ >=9#$0)$ * "!# !#$%&' 8"#0%#0# A = [aij] .! 8". -) ./.!.($-)
aij = 0, +-! i > j6
A =


a11 a12 a13 . . . a1 n−1 a1n
0 a22 a23 . . . a2 n−1 a2n
0 0 a33 . . . a3 n−1 a3n
6
6
6
6
6
6
6
6
6
6
6
6
6
6
6
0 0 0 . . . an−1 n−1 an−1 n
0 0 0 . . . 0 ann


B =


1 2 3 4
0 −1 5 7
0 0 9 8
0 0 0 −3


<A
 !" !"#$%& !"#$%&'#! ($)*!"+! ' (!" !"#$%& )("*$"*" A = [aij] +! )(+ ,- +.+!+/#,-
aij = 00 1,! i < j2
A =


a11 0 0 . . . 0 0
a21 a22 0 . . . 0 0
a31 a32 a33 . . . 0 0
2
2
2
2
2
2
2
2
2
2
2
2
2
2
2
an−1 1 an−1 2 an−1 3 . . . an−1 n−1 0
an 1 an 2 an 3 . . . an n−1 ann


B =


1 0 0 0
3 −1 0 0
−2 6 9 0
5 7 0 −3


,-. /+01$2"# 3* &4# 5#0!"6
 !" !"#$%& )("*$"*" A = [aij] 3,*+ -+$ !(.#%3.%1"*" n 4+&+- 3,$ -% !+-!"2 5 !"#$%& )(+
$+-(.#" *+--"- ,3+$"67+-0 + )(+ ' $+3$+-+/#"*" 3,$ An0 ' 18"!"*" *+ 3,#9/1%" n *" !"#$%&
A2
:+ A2 = A0 *%&;-+ )(+ A ' (!" 5#0!"6 (3*47+0*$0*2
:+ Ap = 00 ,/*+ p ' %/#+%$, 3,-%#%4,0 *%&;-+ )(+ A ' (!" 5#0!"6 8"9"'7+0*$0*2
:;*47'+ ,<= :+/*, A =
(
1 2
4 3
)
2 <+#+$!%/+ A2 + A32
:;*47'+ ,>= :+/*, A =
(
10 −25
4 −10
)
2 =".1(.+ A22
:;*47'+ ,?= :+/*, A =

 2 −1 1−2 3 −2
−4 4 −3


2 =".1(.+ A22
:;*47'+ ,@= :+/*, C =

 3 0 0−2 2 0
1 1 −3


+ D =

 −1 0 0−3 4 0
2 1 1


2 =".1(.+ E = CD2
>>