Saved Bookmarks
| 1. |
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 |
|
Answer» A= ⎣ ⎢ ⎢ ⎡
1 1
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
⎦ ⎥ ⎥ ⎤
|
|