Hw 51.61 41 1 2 2

sx i6xE9

L's Itad be L 6 1.5 1

A T LETEh A 5 1 711

X 3 XE I

check 3 t C 4 2

5.3 61 4 15 6 9

3 Xc 13 24 3 4

2X c 2X at Xz I

2x 13 2 1 3 3

I E'tp

i S

z l 2 0 Ito 710 a

320 30230 l l l 3 3f io c

1 I 2 3 4

0 i I l

l ioc Z 3 14

1 00 I O l

4 i3 4

I O l

AE I 1 V

4

I 0 I

L it

4

O

L

E A b

L IIg x I E 4 4 7

check s I t 3 4 t C 71 4

2 t t 2 4 t C7 I

2 t t 3 4 1 7 3

13 K 3 2 b

it xu be

e II

3

D

24 45 3g be

Xu 34th be

cheek A L ad seethe

4 L Ic ii Hi

It is consistent for all b and be

15 X 2 21 5 3b

UX 5 2 18 3 62

x 13 2 3 3 63

I I 3 40 0 20

3 3 3 bag O

i

Iwhen bit be 14 0 4 batb

the linear system is consistent

21opt.vn let A Ef be a

homogeneous linear system of n

linear equations is in unknown

that has only the trivial solution

Prove that if k is any positive

integer then the linear system

Ak2 5 also has onf the

trivial solution

Trott Since AI 58 has oftrivial solution A

B invertible Ak is alsoinvertible let CAk is itsinverse Now let IT be

any solution for EI IB

that is Akioconsider fate j E Yb

Act Ah AES I

45 Ak 1 AI

7

I CAXT P

A 3 If P

So Ake 3 has of trivial

solution