Compute 4A?- 6B² matrix for the following:
[3 2 -1 [3 A = 7 -6 0 B = 0 6. 15 2 -7 9 51 3 1]
[9
Answers
Answer:
A=
⎣
⎢
⎢
⎡
1
1
2
1
2
−1
1
−3
3
⎦
⎥
⎥
⎤
To Prove : A
3
−6A
2
+5A+11I=O
Consider, A
2
=
⎣
⎢
⎢
⎡
1
1
2
1
2
−1
1
−3
3
⎦
⎥
⎥
⎤
⎣
⎢
⎢
⎡
1
1
2
1
2
−1
1
−3
3
⎦
⎥
⎥
⎤
=
⎣
⎢
⎢
⎡
1+1+2
1+2−6
2−1+6
1+2−1
1+4+3
2−2−3
1−3+3
1−6−9
2+3+9
⎦
⎥
⎥
⎤
⇒A
2
=
⎣
⎢
⎢
⎡
4
−3
7
2
8
−3
1
−14
14
⎦
⎥
⎥
⎤
Now, A
3
=A
2
A
=
⎣
⎢
⎢
⎡
4
−3
7
2
8
−3
1
−14
14
⎦
⎥
⎥
⎤
⎣
⎢
⎢
⎡
1
1
2
1
2
−1
1
−3
3
⎦
⎥
⎥
⎤
=
⎣
⎢
⎢
⎡
4+2+2
−3+8−28
7−3+28
4+4−1
−3+16+14
7−6−14
4−6+3
−3−24−42
7+9+42
⎦
⎥
⎥
⎤
A
3
=
⎣
⎢
⎢
⎡
8
−23
32
7
27
−13
1
−69
58
⎦
⎥
⎥
⎤
itzurchocolate said thanks for the answer
Answer:
A=
⎣
⎢
⎢
⎡
1
1
2
1
2
−1
1
−3
3
⎦
⎥
⎥
⎤
To Prove : A
3
−6A
2
+5A+11I=O
Consider, A
2
=
⎣
⎢
⎢
⎡
1
1
2
1
2
−1
1
−3
3
⎦
⎥
⎥
⎤
⎣
⎢
⎢
⎡
1
1
2
1
2
−1
1
−3
3
⎦
⎥
⎥
⎤
=
⎣
⎢
⎢
⎡
1+1+2
1+2−6
2−1+6
1+2−1
1+4+3
2−2−3
1−3+3
1−6−9
2+3+9
⎦
⎥
⎥
⎤
⇒A
2
=
⎣
⎢
⎢
⎡
4
−3
7
2
8
−3
1
−14
14
⎦
⎥
⎥
⎤
Now, A
3
=A
2
A
=
⎣
⎢
⎢
⎡
4
−3
7
2
8
−3
1
−14
14
⎦
⎥
⎥
⎤
⎣
⎢
⎢
⎡
1
1
2
1
2
−1
1
−3
3
⎦
⎥
⎥
⎤
=
⎣
⎢
⎢
⎡
4+2+2
−3+8−28
7−3+28
4+4−1
−3+16+14
7−6−14
4−6+3
−3−24−42
7+9+42
⎦
⎥
⎥
⎤
A
3
=
⎣
⎢
⎢
⎡
8
−23
32
7
27
−13
1
−69
58
⎦
⎥
⎥
⎤