Begin2.DVI

10-18. Evaluate the following determinants:

(a)

∣∣

∣∣3 2

4 − 1

∣∣

∣∣ (b)

∣∣

∣∣ 0 3

−2 0

∣∣

∣∣ (c)

∣∣

∣∣1 2

3 4

∣∣

∣∣

10-19. Evaluate the following determinants:

(a)

∣∣

∣∣

∣∣

1 3 − 1

0 1 2

1 0 1

∣∣

∣∣

∣∣ (b)

∣∣

∣∣

∣∣

0 1 2

− 1 − 1 − 1

2 0 3

∣∣

∣∣

∣∣ (c)

∣∣

∣∣

∣∣

2 0 − 1

− 1 − 1 − 1

2 4 3

∣∣

∣∣

∣∣

10-20. Given

A=





1 1 1

2 4 1

3 2 4





(a) Find all minors Mij (b) Find all cofactors Cij (c) Calculate AC T

10-21. Evaluate the determinant

∣∣

∣∣

∣∣

2 x 3 x 4 x

y −y 0

z 3 z 2 z

∣∣

∣∣

∣∣

10-22. Evaluate the following determinants:

(a)

∣∣

∣∣

∣∣

1 2 3

2 4 6

−1 0 3

∣∣

∣∣

∣∣

(c)

∣∣

∣∣

∣∣

∣

1 0 −1 3

0 1 1 2

0 0 3 4

−1 0 −2 5

∣∣

∣∣

∣∣

∣

(e)

∣∣

∣∣

∣∣

∣

a 1 0 0 0

 1 a 2 0 0

 2  3 a 3 0

 4  5  6 a 4

∣∣

∣∣

∣∣

∣

(b)

∣∣

∣∣

∣∣

2 0 3

−1 0 π

e 0. 32

∣∣

∣∣

∣∣

(d)

∣∣

∣∣

∣∣

∣

a 1  1  2  3

0 a 2  4  5

0 0 a 3  6

0 0 0 a 4

∣∣

∣∣

∣∣

∣

(f)

∣∣

∣∣

∣∣

∣

25 0 −25 75

0 5 5 10

0 0 6 8

−5 0 −10 25

∣∣

∣∣

∣∣

∣

(g) How is the determinant in (f) related to the determinant in (c)?

10-23.

(a) Find the inverse of

Z=

[

z 11 z 12

z 21 z 22

]

(b) What condition must be satisfied for the inverse to exist?