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7/25/2019 Matrices 2x2 3x3 4x4 5x5
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8 -2 0 100
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7/25/2019 Matrices 2x2 3x3 4x4 5x5
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7/25/2019 Matrices 2x2 3x3 4x4 5x5
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7/25/2019 Matrices 2x2 3x3 4x4 5x5
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7/25/2019 Matrices 2x2 3x3 4x4 5x5
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7/25/2019 Matrices 2x2 3x3 4x4 5x5
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7/25/2019 Matrices 2x2 3x3 4x4 5x5
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7/25/2019 Matrices 2x2 3x3 4x4 5x5
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7/25/2019 Matrices 2x2 3x3 4x4 5x5
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7/25/2019 Matrices 2x2 3x3 4x4 5x5
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7/25/2019 Matrices 2x2 3x3 4x4 5x5
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7/25/2019 Matrices 2x2 3x3 4x4 5x5
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7/25/2019 Matrices 2x2 3x3 4x4 5x5
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7/25/2019 Matrices 2x2 3x3 4x4 5x5
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7/25/2019 Matrices 2x2 3x3 4x4 5x5
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7/25/2019 Matrices 2x2 3x3 4x4 5x5
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7/25/2019 Matrices 2x2 3x3 4x4 5x5
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7/25/2019 Matrices 2x2 3x3 4x4 5x5
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7/25/2019 Matrices 2x2 3x3 4x4 5x5
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7/25/2019 Matrices 2x2 3x3 4x4 5x5
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7/25/2019 Matrices 2x2 3x3 4x4 5x5
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7/25/2019 Matrices 2x2 3x3 4x4 5x5
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7/25/2019 Matrices 2x2 3x3 4x4 5x5
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7/25/2019 Matrices 2x2 3x3 4x4 5x5
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7/25/2019 Matrices 2x2 3x3 4x4 5x5
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7/25/2019 Matrices 2x2 3x3 4x4 5x5
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*D+,0 *D+,0 ! /3= *D+,0
*D+,0 *D+,0 ! /4= *D+,0
*D+,0 *D+,0 ! /5= *D+,0
*D+,0 *D+,0 ! /6= *D+,0*D+,0 *D+,0 ! /7= *D+,0
*D+,0 *D+,0 ! /8= *D+,0
*D+,0 *D+,0
*D+,0 *D+,0
*D+,0 *D+,0
*D+,0 *D+,0
*D+,0 *D+,0 ! /2= *D+,0
*D+,0 *D+,0 ! /3= *D+,0*D+,0 *D+,0 ! /4= *D+,0
*D+,0 *D+,0 ! /5= *D+,0
*D+,0 *D+,0 ! /6= *D+,0
*D+,0 *D+,0 ! /7= *D+,0
*D+,0 *D+,0 ! /8= *D+,0
*D+,0 *D+,0 ! /9= *D+,0
*D+,0 *D+,0
*D+,0 *D+,0
*D+,0 *D+,0
*D+,0 *D+,0 ! /2= *D+,0
*D+,0 *D+,0 ! /3= *D+,0
*D+,0 *D+,0 ! /4= *D+,0
*D+,0 *D+,0 ! /5= *D+,0
*D+,0 *D+,0 ! /6= *D+,0
*D+,0 *D+,0 ! /7= *D+,0
*D+,0 *D+,0 ! /8= *D+,0
*D+,0 *D+,0 ! /9= *D+,0
*D+,0 *D+,0 ! /10= *D+,0
*D+,0 *D+,0
*D+,0 *D+,0
*D+,0 *D+,0 ! /2= *D+,0
*D+,0 *D+,0 ! /3= *D+,0
*D+,0 *D+,0 ! /4= *D+,0
*D+,0 *D+,0 ! /5= *D+,0
7/25/2019 Matrices 2x2 3x3 4x4 5x5
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*D+,0 *D+,0 ! /6= *D+,0
*D+,0 *D+,0 ! /7= *D+,0
*D+,0 *D+,0 ! /8= *D+,0
*D+,0 *D+,0 ! /9= *D+,0
*D+,0 *D+,0 ! /10= *D+,0
*D+,0 *D+,0 ! /11= *D+,0
*D+,0 *D+,0
*D+,0 *D+,0 ! /2= *D+,0
*D+,0 *D+,0 ! /3= *D+,0
*D+,0 *D+,0 ! /4= *D+,0
*D+,0 *D+,0 ! /5= *D+,0
*D+,0 *D+,0 ! /6= *D+,0
*D+,0 *D+,0 ! /7= *D+,0
*D+,0 *D+,0 ! /8= *D+,0
*D+,0 *D+,0 ! /9= *D+,0*D+,0 *D+,0 ! /10= *D+,0
*D+,0 *D+,0 ! /11= *D+,0
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7/25/2019 Matrices 2x2 3x3 4x4 5x5
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# # &2#
1 1 4 4 4
2 2 7 14 28
3 3 9 27 81
4 4 10 40 160
5 5 9 45 2256 6 7 42 252
7 7 4 28 196
8 0 0 0 0
9 0 0 0 0
10 0 0 0 0
11 0 0 0 0
12 0 0 0 0
13 0 0 0 0
14 0 0 0 0
15 0 0 0 0$ 28 50 200 946
= 7
# #1 #2
1 1 4 7.1428571429 3.9285714286
2 2 7 7.1428571429 7.1428571429
3 3 9 7.1428571429 9.0714285714
4 4 10 7.1428571429 9.7142857143
5 5 9 7.1428571429 9.0714285714
6 6 7 7.1428571429 7.1428571429
7 7 4 7.1428571429 3.9285714286
8 0 0 7.1428571429 -0.5714285714
9 0 0 7.1428571429 -0.5714285714
10 0 0 7.1428571429 -0.5714285714
11 0 0 7.1428571429 -0.5714285714
12 0 0 7.1428571429 -0.5714285714
13 0 0 7.1428571429 -0.5714285714
14 0 0 7.1428571429 -0.5714285714
15 0 0 7.1428571429 -0.5714285714
#1=/2%/3
#2=/2%/3%/4&2
#3=/2%/3%/4&2%/5
#4=/2%/3%/4&2%/5&3%
#5=/2%/3%/4&2%/5&3%/6
#6=/2%/3%/4&2%/5&3%/6&4%
#7=/2%/3%/4&2%/5&3%/6&4%/7
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#8=/2%/3%/4&2%/5&3%/6&4%/7&5%
#9=/2%/3%/4&2%/5&3%/6&4%/7&5%/8&
#10=/2%/3%/4&4%/5&3%/6&4%/7&5%/8&6%/
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&3# &4# &5# &6#
4 4 4 4
56 112 224 448
243 729 2187 6561
640 2560 10240 40960
1125 5625 28125 1406251512 9072 54432 326592
1372 9604 67228 470596
0 0 0 0
0 0 0 0
0 0 0 0
0 0 0 0
0 0 0 0
0 0 0 0
0 0 0 0
0 0 0 04952 27706 162440 985786
#3 #4 #5 #6
*D+,0 *D+,0 *D+,0 *D+,0
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*D+,0 *D+,0 *D+,0 *D+,0
*D+,0 *D+,0 *D+,0 *D+,0
&3
/6&4
&4%/7&5
/7&5%/8&6
&5%/8&6%/9&7
7/25/2019 Matrices 2x2 3x3 4x4 5x5
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8&6%/9&7%/10&8
6%/9&7%/10&8%/11&9
&7%/10&8%/11&9%/12&10
7/25/2019 Matrices 2x2 3x3 4x4 5x5
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&7# &8# &9# &10#
4 4 4 4
896 1792 3584 7168
19683 59049 177147 531441
163840 655360 2621440 10485760
703125 3515625 17578125 878906251959552 11757312 70543872 423263232
3294172 23059204 161414428 1129900996
0 0 0 0
0 0 0 0
0 0 0 0
0 0 0 0
0 0 0 0
0 0 0 0
0 0 0 0
0 0 0 06141272 39048346 252338600 1652079226
#7 #8 #9 #10
*D+,0 *D+,0 *D+,0 *D+,0
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7/25/2019 Matrices 2x2 3x3 4x4 5x5
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&2 &3 &4 &5
1 1 1 1
4 8 16 32
9 27 81 243
16 64 256 1024
25 125 625 312536 216 1296 7776
49 343 2401 16807
0 0 0 0
0 0 0 0
0 0 0 0
0 0 0 0
0 0 0 0
0 0 0 0
0 0 0 0
0 0 0 0140 784 4676 29008
'1 '2 '3 '4
-3.1428571429 0.0714285714 *D+,0 *D+,0
-0.1428571429 -0.1428571429 *D+,0 *D+,0
1.8571428571 -0.0714285714 *D+,0 *D+,0
2.8571428571 0.2857142857 *D+,0 *D+,0
1.8571428571 -0.0714285714 *D+,0 *D+,0
-0.1428571429 -0.1428571429 *D+,0 *D+,0
-3.1428571429 0.0714285714 *D+,0 *D+,0
-7.1428571429 0.5714285714 *D+,0 *D+,0
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ala e alore
&6 &7 &8
1 1 1
64 128 256
729 2187 6561
4096 16384 65536
15625 78125 39062546656 279936 1679616
117649 823543 5764801
0 0 0
0 0 0
0 0 0
0 0 0
0 0 0
0 0 0
0 0 0
0 0 0184820 1200304 7907396
'5 '6 '7
*D+,0 *D+,0 *D+,0
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7/25/2019 Matrices 2x2 3x3 4x4 5x5
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&9 &10 &11
1 1 1
512 1024 2048
19683 59049 177147
262144 1048576 4194304
1953125 9765625 4882812510077696 60466176 362797056
40353607 282475249 1977326743
0 0 0
0 0 0
0 0 0
0 0 0
0 0 0
0 0 0
0 0 0
0 0 052666768 353815700 2393325424
'8 '9 '10
*D+,0 *D+,0 *D+,0
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$1
$2
$3
$4
$5
$6
$7
$8
$9
7/25/2019 Matrices 2x2 3x3 4x4 5x5
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$10
$11
$12
$13
$14
$15
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&12 &13 &14
1 1 1
4096 8192 16384
531441 1594323 4782969
16777216 67108864 268435456
244140625 1220703125 61035156252176782336 13060694016 78364164096
13841287201 96889010407 678223072849
0 0 0
0 0 0
0 0 0
0 0 0
0 0 0
0 0 0
0 0 0
0 0 016279522916 111239118928 762963987380
('&2)1 ('&2)2 ('&2)3
9.8775510204 0.0051020408 *D+,0
0.0204081633 0.0204081633 *D+,0
3.4489795918 0.0051020408 *D+,0
8.1632653061 0.0816326531 *D+,0
3.4489795918 0.0051020408 *D+,0
0.0204081633 0.0204081633 *D+,0
9.8775510204 0.0051020408 *D+,0
51.0204081633 0.3265306122 *D+,0
51.0204081633 0.3265306122 *D+,0
51.0204081633 0.3265306122 *D+,0
51.0204081633 0.3265306122 *D+,0
51.0204081633 0.3265306122 *D+,0
51.0204081633 0.3265306122 *D+,0
51.0204081633 0.3265306122 *D+,0
51.0204081633 0.3265306122 *D+,0
9.8775510204 0.0051020408 *D+,0
9.8979591837 0.0255102041 *D+,0
13.3469387755 0.0306122449 *D+,0
21.5102040816 0.112244898 *D+,0
24.9591836735 0.1173469388 *D+,0
24.9795918367 0.137755102 *D+,0
34.8571428571 0.1428571429 *D+,0
85.8775510204 0.4693877551 *D+,0
136.8979591837 0.7959183673 *D+,0
7/25/2019 Matrices 2x2 3x3 4x4 5x5
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187.9183673469 1.1224489796 *D+,0
238.9387755102 1.4489795918 *D+,0
289.9591836735 1.7755102041 *D+,0
340.9795918367 2.1020408163 *D+,0
392 2.4285714286 *D+,0
443.0204081633 2.7551020408 *D+,0
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&15 &16 &17
1 1 1
32768 65536 131072
14348907 43046721 129140163
1073741824 4294967296 17179869184
30517578125 152587890625 762939453125470184984576 2821109907456 16926659444736
4747561509943 33232930569601 232630513987207
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7/25/2019 Matrices 2x2 3x3 4x4 5x5
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&18 &19 &20
1 1 1
262144 524288 1048576
387420489 1162261467 3486784401
68719476736 274877906944 1099511627776
3814697265625 19073486328125 95367431640625101559956668416 609359740010496 3656158440062980
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7/25/2019 Matrices 2x2 3x3 4x4 5x5
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('&2)10
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