620188151058770 algebra and geometry

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Algebra and solid Exam Q(13)A Tower guy wire is anchored by mean of a ring at A .The tension in the wire is 2600N determine the components I I Fz A ->(-3,4,0) , B (0,0,12) AB = B - A = (0,0,12)-(- 3,4,0) = (3,-4,12) F=

2600

(3-4,12) = ^ 2 0 (3 , _ 4 j +12K)

J 32 + 42 + 122

F = 600 i - 800 j + 2400 K

Q (14) Solve the following system of linear equations using the inverse m atrix where 4X+Y=0 , X+2Z=15 , Y-7Z=0 "-2 7 1" The cofactor m atrix 7 -28 -4

Adj (A) = 7 -28 -8 1 -4 -1 f Xl f 2 Y = -7 1 1

UJ

iH

<M

N

CVJ i

r

1 00 1

CO

4 1 0 |A| = 1 0 2 =- l 0 1 -7

f 2

" A =R

“ -7 28 --1 4

-7 -2^ (-105) 28 8 15 = 480 loj I 60 J X a a

Q(15)Prove that

a a X a = (X + 2 a X X -a )2 a X

= (X + 2aXx - a f

9 + 0)

X + 2a a a X + 2a X a X + 2a a X

11

C1 +C2+c 3

|1 a a |1 a X a = (X + 2alO X - a |l a X |o 0

a 0 X -a

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