Editorial - Matwa - Soal TKA 2

Problem 1

Find the mean.

μ=(8+9+10+11+12+12+12+14)/8=11

(σ^2)=((∑_^)(x-μ)2)/n=(9+4+1+1+1+1+9)/8=3.25

Problem 2

μ=(78⋅12+80⋅(72-12))/72=79.67≈79.7

Problem 3

p=100-(40+15+12+10+15)=8

n=8/40⋅120=24

Problem 4

(C_10^14)=14!/(10!⋅4!)=1001

Problem 5

why

μ=5

(σ^)=√(,11)/2

Problem 6

1. ⊤

2. ⊥

3. ⊤

4. ⊤

Problem 7

A=[[-2,-4],[5,3]]

B=[[-1,3],[1,4]]

C=[[2,-1],[4,2]]

D=2⋅A-B-3*C

D=[[-4,-8],[10,6]]+[[1,-3],[-1,-4]]+[[-6,3],[-12,-6]]=[[-9,-8],[-3,-4]]

|D|=3*6-24=12

Problem 8

R=[[3,4],[5,8]]+[[0,-2],[6,-1]]=[[3,2],[11,7]]

R(-1)=1/(-1)⋅[[7,-2],[-11,3]]=[[-7,2],[11,-3]]

Problem 9

A*X=B

X=A(-1)⋅B

A(-1)=1/5*[[3,1],[-2,1]]

X=1/5⋅[[3,1],[-2,1]]⋅[[-7,-3],[11,4]]=[[…,…],[…,2]]

Problem 10

[[-5,-7],[2,6]]-2*A=[[-1,-3],[4,10]]

[[-5,-7],[2,6]]-[[2*a,2*b],[2*c,2*d]]=[[-1,-3],[4,10]]

-5-2*a=-1

∴a=-2

-7-2*b=-3

∴b=-2

2-2*c=4

∴c=-1

6-2*d=10

∴d=-2

∴|A|=a*d-b*c=4-2=2

Yippee!