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ira [324]
1 year ago
5

There are 49 students had their lunch in the cafeteria. One-

Mathematics
1 answer:
Harman [31]1 year ago
3 0
7 students brought lunch from home
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Given vectors u = (−1, 2, 3) and v = (3, 4, 2) in R 3 , consider the linear span: Span{u, v} := {αu + βv: α, β ∈ R}. Are the vec
julia-pushkina [17]

Answer:

(2,6,6) \not \in \text{Span}(u,v)

(-9,-2,5)\in \text{Span}(u,v)

Step-by-step explanation:

Let b=(b_1,b_2,b_3) \in \mathbb{R}^3. We have that b\in \text{Span}\{u,v\} if and only if we can find scalars \alpha,\beta \in \mathbb{R} such that \alpha u + \beta v = b. This can be translated to the following equations:

1. -\alpha + 3 \beta = b_1

2.2\alpha+4 \beta = b_2

3. 3 \alpha +2 \beta = b_3

Which is a system of 3 equations a 2 variables. We can take two of this equations, find the solutions for \alpha,\beta and check if the third equationd is fulfilled.

Case (2,6,6)

Using equations 1 and 2 we get

-\alpha + 3 \beta = 2

2\alpha+4 \beta = 6

whose unique solutions are \alpha =1 = \beta, but note that for this values, the third equation doesn't hold (3+2 = 5 \neq 6). So this vector is not in the generated space of u and v.

Case (-9,-2,5)

Using equations 1 and 2 we get

-\alpha + 3 \beta = -9

2\alpha+4 \beta = -2

whose unique solutions are \alpha=3, \beta=-2. Note that in this case, the third equation holds, since 3(3)+2(-2)=5. So this vector is in the generated space of u and v.

4 0
2 years ago
Solve the right triangle : A=22°, c=8
coldgirl [10]

hope it helps you!!!!!!!!!!!!

8 0
3 years ago
I know it is basic but I need help<br><br>11m+13=m+23
zloy xaker [14]

Answer:

m = 1

Step-by-step explanation:

11m + 13 = m + 23

<u>Get m by itself by subtracting m from both sides. </u>

10m + 13 = 23

<u>Subtract 13 from both sides.</u>

10m = 10

<u>DIvide by 10.</u>

m = 1

8 0
3 years ago
Read 2 more answers
Which of the following represents "the square of the sum of a number and 4 is 36"? x2 + 42 = 36 x2 + 4 = 36 (x + 4)2 = 36
MrRa [10]
<span>"the square of the sum of a number and 4 is 36"
=
</span><span>(x + 4)^2 = 36


</span>
5 0
3 years ago
Read 2 more answers
Simplify the trigonometric expression sin(4x) +2 sin(2x) using Double-Angle<br> Identities.
emmasim [6.3K]

Answer:

8sin(x)cos³(x)

Step-by-step explanation:

sin(4x) +2 sin(2x)  = 2sin(2x)*cos(2x) + 2sin(2x) = 2sin(2x)(cos2x + 1)=

= 2sin(2x)(cos²x - sin²x + cos²x + sin²x)=²2sin(2x)*(2cos²x)=

= 4*2sin(x)*cos(x)*cos²(x)= 8sin(x)cos³(x)

6 0
2 years ago
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