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arlik [135]
3 years ago
6

Let u,v,wu,v,w be three linearly independent vectors in R7R7. Determine a value of kk, k=k= , so that the set S={u−3v,v−2w,w−ku}

S={u−3v,v−2w,w−ku} is linearly dependent.
Mathematics
1 answer:
11Alexandr11 [23.1K]3 years ago
6 0

Answer:

1/6

Step-by-step explanation:

For a set of vectors a, b and c to be linearly dependent, the linear combination of the set of vectors must be zero.

C1a + C2b + C3c = 0

From the question, we are given the set S={u−3v,v−2w,w−ku}, the corresponding vectors are a(0, -3, 1), b(-2,1,0) and c(1,0,-k)

The values in parenthesis are the ccoefficients of w, v and u respectively.

On writing this vector as a linear combination, we will have;

C1(0, -3, 1) + C2(-2,1,0) + C3(1,0,-k) = (0,0,0)

0-2C2+C3 = 0........ 1

-3C1+C2 = 0 ........... 2

C1-kC3 = 0 ….......... 3

From equation 2, 3C1 = C2

Substituting into 1, -2(3C1)+C3 = 0

-6C1+C3 = 0

-6C1 = -C3

6C1 = C3.…..4

Substitute 4 into 3 to have

C1-k(6C1) = 0

C1 = k6C1

6k = 1

k = 1/6

Hence the value of k for the set of vectors to be linearly dependent is 1/6

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prime1

/prīm/

Learn to pronounce

See definitions in:

All

Mathematics

Religion

Printing

Fencing

Weapons

Building

Mechanics

Motoring

Biochemistry

adjective

1.

of first importance; main.

"her prime concern is the well-being of the patient"

Similar:

main

chief

key

primary

central

principal

foremost

first

most important

paramount

major

dominant

supreme

overriding

cardinal

preeminent

ultimate

number-one

fundamental

basic

essential

elemental

vital

Opposite:

secondary

subordinate

2.

of the best possible quality; excellent.

"prime cuts of meat"

Similar:

top-quality

highest quality

top

top-tier

best

first-class

first-rate

high-grade

grade A

superior

supreme

flawless

choice

select

finest

superlative

peak

optimal

model

excellent

marvelous

magnificent

superb

fine

wonderful

exceptional

formidable

top of the range

top of the line

tip-top

A1

stellar

top-notch

Opposite:

inferior

noun

1.

a state or time of greatest strength, vigor, or success in a person's life.

"you're in the prime of life"

Similar:

heyday

best days/years

day

time

prime of one's life

maturity

youth

springtime

salad days

bloom

flowering

full flowering

perfection

peak

pinnacle

height

high point/spot

zenith

ascendancy

2.

CHRISTIAN CHURCH

a service forming part of the Divine Office, traditionally said (or chanted) at the first hour of the day (i.e., 6 a.m.), but now little used.prime1

/prīm/

Learn to pronounce

See definitions in:

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Mathematics

Religion

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adjective

1.

of first importance; main.

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Similar:

main

chief

key

primary

central

principal

foremost

first

most important

paramount

major

dominant

supreme

overriding

cardinal

preeminent

ultimate

number-one

fundamental

basic

essential

elemental

vital

Opposite:

secondary

subordinate

2.

of the best possible quality; excellent.

"prime cuts of meat"

Similar:

top-quality

highest quality

top

top-tier

best

first-class

first-rate

high-grade

grade A

CHRISTIAN CHURCH

a service forming part of the Divine Office, traditionally said (or chanted) at the first hour of the day (i.e., 6 a.m.), but now little used.

8 0
3 years ago
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