用Matlab学习线性代数 - 线性方程组与矩阵代数概要(10)

>> A3=A^6+A; A3 =

119 1 86 1 64 0 103 1 1 119 1 103 0 64 1 86 86 1 63 1 47 0 73 0 1 103 1 93 64 0 47 1 0 64 0 56 103 1 73 0 1 86 0 73 >> sum(sum(A3(1:8,1:8))) ans = 2362

>> A4=A^8+A A4 =

799 1 577 1 1 799 1 697 577 1 418 1 1 697 1 614 436 0 316 1 1 56 38 1 1 38 56 1 0 47 436 0 0 436 316 0 1 381 243 1 0 73 56 0 1 47 93 1 1 63 697 1 1 577 501 0 0 501 381 0

0 436 0 381 1 243 1 316 697 1 501 0 381 1 614 1 1 577 0 501 0 316 1 418 >> sum(sum(A4(1:8,1:8))) ans = 15800 (4)

>> A5=A^3+A A5 =

0 8 0 7 8 0 6 0 0 6 0 6 7 0 6 0 0 3 0 5 3 0 2 0 0 7 0 4 6 0 3 0

>> sum(sum(A5(1:8,1:8))) ans = 154

0 3 3 0 0 2 5 0 0 4 4 0 0 5 2 0 0 6 7 0 0 3 4 0 0 2 5 0 0 6 6 0

>> A6=A^5+A A6 =

0 47 0 41 0 24 0 34 47 0 34 0 0 34 0 31 41 0 31 0 0 24 0 24 24 0 17 0 0 41 0 33 34 0 23 0 >> sum(sum(A6(1:8,1:8))) ans = 922

>> A7=A^7+A A7 =

0 309 0 270 309 0 223 0 0 223 0 197 270 0 197 0 24 0 0 17 24 0 0 16 16 0 0 24 17 0 0 167 0 0 120 0 41 0 0 23 33 0 0 17 24 0 0 31 31 0 0 223 270 0 0 159 232 0

167 150 0 167 0 150 0 95 0 120 167 0 120 0 95 0 150 0 0 270 0 232 0 150 0 197 223 0 159 0 120 0 197 0 > sum(sum(A7(1:8,1:8))) ans = 6098 >> A^2 ans =

3 0 2 0 0 3 0 2 2 0 2 0 0 2 0 3 1 0 1 0 0 1 0 1 2 0 1 0 0 2 0 1

1 0 0 1 1 0 0 1 2 0 0 2 1 0 0 1 2 0 0 2 1 0 0 1 1 0 0 1 3 0 0 2 >> A^4 ans =

18 0 13 0 9 0 15 0 0 13 0 9 0 15 0 >> A^6 ans =

119 0 86 0 64 18 0 0 10 15 0 0 7 9 0 0 10 13 0 0 86 0 0 63 0 0 47 15 0 0 7 15 0 0 7 8 0 0 8 10 0 0 64 0 0 47 93 0 0 38 9 0 0 10 8 0 0 8 7 0 0 15 7 0 0 103 64 0 0 73 0 0 56 0 0 7 0 0 86 0 73 0

13 10 10 119 103 103 56