1answer.
Ask question
Login Signup
Ask question
All categories
  • English
  • Mathematics
  • Social Studies
  • Business
  • History
  • Health
  • Geography
  • Biology
  • Physics
  • Chemistry
  • Computers and Technology
  • Arts
  • World Languages
  • Spanish
  • French
  • German
  • Advanced Placement (AP)
  • SAT
  • Medicine
  • Law
  • Engineering
oksano4ka [1.4K]
3 years ago
12

Determine all real values of p such that the set of all linear combination of u = (3, p) and v = (1, 2) is all of R2. Justify yo

ur answer.
Mathematics
1 answer:
Rama09 [41]3 years ago
7 0

Answer:

p ∈ IR - {6}

Step-by-step explanation:

The set of all linear combination of two vectors ''u'' and ''v'' that belong to R2

is all R2 ⇔

u\neq 0_{R2}      

v\neq 0_{R2}

And also u and v must be linearly independent.

In order to achieve the final condition, we can make a matrix that belongs to R^{2x2} using the vectors ''u'' and ''v'' to form its columns, and next calculate the determinant. Finally, we will need that this determinant must be different to zero.

Let's make the matrix :

A=\left[\begin{array}{cc}3&1&p&2\end{array}\right]

We used the first vector ''u'' as the first column of the matrix A

We used the  second vector ''v'' as the second column of the matrix A

The determinant of the matrix ''A'' is

Det(A)=6-p

We need this determinant to be different to zero

6-p\neq 0

p\neq 6

The only restriction in order to the set of all linear combination of ''u'' and ''v'' to be R2 is that p\neq 6

We can write : p ∈ IR - {6}

Notice that is p=6 ⇒

u=(3,6)

v=(1,2)

If we write 3v=3(1,2)=(3,6)=u , the vectors ''u'' and ''v'' wouldn't be linearly independent and therefore the set of all linear combination of ''u'' and ''b'' wouldn't be R2.

You might be interested in
Find x.<br><br><br><br> 1.5<br> 2<br> <img src="https://tex.z-dn.net/?f=%5Csqrt%7B3%7D" id="TexFormula1" title="\sqrt{3}" alt="\
Vanyuwa [196]

Answer:

1.5

Step-by-step explanation:

3 0
3 years ago
Nine times a number divided by 2 equals 54.
bazaltina [42]

x = the unknown number

\frac{9x}{2} =54

nine <u>times</u>(multiplication) a number(x) divided(division) by 2 equals(=) 54,

so 9x is divided by 2

4 0
3 years ago
What is the calculation for determining simple interest and compound interest? Borrowing if borrowed $20,000 for 5 years at a 4%
yarga [219]

Answer:

If using simple interest, the formula is:

= Amount * ( 1 + rate * time)

= 20,000 * ( 1 + 4% * 5)

= $24,000

Interest = Balance after 5 years - Investment

= 24,000 - 20,000

= $4,000

Using Compound Interest:

= Amount * ( 1 + rate)^time

= 20,000 * ( 1 + 4%)⁵

= $24,333.06

Interest = 24,333.06 - 20,000

= $4,333.06

6 0
3 years ago
What is 3/5 times 1/3 in simplest form
djverab [1.8K]
3/5×1/3=1/5×1/1=1/5 so 1/5 is you answer
8 0
3 years ago
Read 2 more answers
In triangle ABC, the length of side AB is 16 inches and the length of side BC is 23 inches. Which of the following could be the
Aleksandr [31]
A 31 inches is the answer because it can't be higher than 39

4 0
3 years ago
Other questions:
  • Someone PLEASE PLEASE HELP!! I need this in one hour!! (20 POINTS)<br><br> PLEASE SOMEONE HELP
    5·2 answers
  • Figure the standard deviation of the distribution of means for a population with a standard deviation of 20 and sample size of 1
    7·1 answer
  • So im working with factoring by grouping and factoring trinomials by grouping in my algebra 2 class i need some help with a 6 qu
    15·1 answer
  • 4 i jedna druga - 2,3 - 3,2= ???
    12·1 answer
  • Another car is 4 years old And has been valued at 2600
    5·1 answer
  • Whats 2+2 :O this is for y'all to get points your welcome &lt;3
    14·1 answer
  • Help me plz will mark brainliest
    15·1 answer
  • A ==(1,2,3,4)kumesinin elemanlarıyla en az iki basamagindaki rakami ayni olan üç basamaklı kaç sayi yazilabilir​
    15·1 answer
  • What is the slope of the line shown?
    12·2 answers
  • HELP HELP HELP HELP HELPPP
    10·2 answers
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!