Systems of Linear Algebraic Equations - Numerical Methods in Engineering with MATLAB - page 96

PROBLEM SET 2.3

1. Let

⎡
⎣

⎤
⎦

⎡
⎣

⎤
⎦

3 12

0 13

− 0 13

3

A = B =

− 12

− 22 − 4 − 22 − 4

(note that B isobtainedbyinterchanging the first two rowsof A ) . Knowing that

⎡
⎣

⎤
⎦

0 . 5 00 . 25

A − 1

=

0 . 3 0 . 40 . 45

− 0 . 1 0 . 2 − 0 . 15

determine B − 1 .

2. Invert the triangular matrices

⎡
⎣

⎤
⎦

⎡
⎣

⎤
⎦

2 4 3
0 65
002

2 00
3 40
4 56

A = B =

3. Invert the triangular matrix

⎡
⎣

⎤
⎦

11 / 21 / 4 1 / 8

0 11 9

0011

/ 31 /

A =

4
0001

/

4. Invert the following matrices:

⎡
⎣

⎤
⎦

⎡
⎣

⎤
⎦

12 4
13 9
1 4 16

4 − 1 0

(a) A = (b) B = − 1 4 − 1

0 − 1 4

5. Invert the matrix

⎡
⎣

⎤
⎦

−

4 21

A = − 21 − 1

1 − 2 4

6. Invert the following matrices with any method:

⎡
⎣

⎤
⎦

⎡
⎣

⎤
⎦

5 − 3 − 1 0 4 − 1 00

− 2111

3

− 1 4 − 1 0

A = B =

− 512 0 − 1 4 − 1

0 8 − 4 − 3 00 − 1 4