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taurus [48]
3 years ago
8

Help please and no links

Mathematics
1 answer:
Rashid [163]3 years ago
7 0

Answer:

I cant see the question :/

Step-by-step explanation:

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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
Rama09 [41]

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.

7 0
3 years ago
Mixed in a drawer are 44 blue​ socks, 88 white​ socks, and 44 gray socks. You pull out two​ socks, one at a​ time, without looki
MrRissso [65]

Answer:

The probability of getting 2 socks of the same color is 1/3.

Step-by-step explanation:

In the drawer,

Number of blue socks = 4

Number of white socks = 8

Number of gray socks = 4

Total number of socks  = 4 + 8 + 4 = 16

Total ways to select 2 socks form 16 socks is

^{16}C_2=\dfrac{16!}{2!(16-2)!}=120

Total ways to select 2 socks of the same color is

T = Possible ways of (2 blue + 2 white +2 gray) socks

  = ^{4}C_2+^{8}C_2+^{4}C_2

  = 6+28+6

  = 40

The probability of getting 2 socks of the same color is

Probability=\dfrac{\text{Total ways to select 2 socks of the same color}}{\text{Total ways to select 2 socks form 16 socks}}

Probability=\dfrac{40}{120}

Probability=\dfrac{1}{3}

Therefore, the probability of getting 2 socks of the same color is 1/3.

3 0
2 years ago
How much can Sophia spend on party favors
Fantom [35]
Think about you have a pizza. you have 6 people and a total of 12 slices. How many can each person get? 2. 

This is the same thing. $2.47 divided by 6 people = $0.46 cents each
8 0
2 years ago
Identify the slope of the line passing through the pair of points (5,2) and (-2,1). *(1point)
olga nikolaevna [1]

Answer:

m= 1/7

Step-by-step explanation:

To solve for slope: y2- y1/ x2- x1 so,

1-2/ -2-5

= -1/ -7

= 1/7

8 0
3 years ago
Read 2 more answers
A is the point with coordinates (3,8) b is the point with coordinates (x,13) the gradient of an is 2.5 .work out the value of x
Solnce55 [7]

Answer:

x = 5

Step-by-step explanation:

The formula for the gradient is given by:

m = (y2 - y1)/(x2 - x1), where two points (x1, y1) and (x2, y2) are given.

Thus if we have a gradient of 2.5 and two points (3, 8) and (x, 13), we can substitute this into the above formula for the gradient to get:

2.5 = (13 - 8)/(x - 3)

2.5(x - 3) = 5 (Multiply both sides by (x - 3))

x - 3 = 2 (Divide both sides by 2.5)

x = 5 (Add 3 to both sides)

Thus, the value of x is 5.

7 0
3 years ago
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