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WARRIOR [948]
3 years ago
11

Which transformation does

Mathematics
1 answer:
inysia [295]3 years ago
8 0
Answer: C Reflection
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Determine if each of the following sets is a subspace of Pn, for an appropriate value of n.
snow_tiger [21]

Answer:

1) W₁ is a subspace of Pₙ (R)

2) W₂ is not a subspace of Pₙ (R)

4) W₃ is a subspace of Pₙ (R)

Step-by-step explanation:

Given that;

1.Let W₁ be the set of all polynomials of the form p(t) = at², where a is in R

2.Let W₂ be the set of all polynomials of the form p(t) = t² + a, where a is in R

3.Let W₃ be the set of all polynomials of the form p(t) = at² + at, where a is in R

so

1)

let W₁ = { at² ║ a∈ R }

let ∝ = a₁t² and β = a₂t²  ∈W₁

let c₁, c₂ be two scalars

c₁∝ + c₂β = c₁(a₁t²) + c₂(a₂t²)

= c₁a₁t² + c²a₂t²

= (c₁a₁ + c²a₂)t² ∈ W₁

Therefore c₁∝ + c₂β ∈ W₁ for all ∝, β ∈ W₁  and scalars c₁, c₂

Thus, W₁ is a subspace of Pₙ (R)

2)

let W₂ = { t² + a ║ a∈ R }

the zero polynomial 0t² + 0 ∉ W₂

because the coefficient of t² is 0 but not 1

Thus W₂ is not a subspace of Pₙ (R)

3)

let W₃ = { at² + a ║ a∈ R }

let ∝ = a₁t² +a₁t  and β = a₂t² + a₂t ∈ W₃

let c₁, c₂ be two scalars

c₁∝ + c₂β = c₁(a₁t² +a₁t) + c₂(a₂t² + a₂t)

= c₁a₁t² +c₁a₁t + c₂a₂t² + c₂a₂t

= (c₁a₁ +c₂a₂)t² + (c₁a₁t + c₂a₂)t ∈ W₃

Therefore c₁∝ + c₂β ∈ W₃ for all ∝, β ∈ W₃ and scalars c₁, c₂

Thus, W₃ is a subspace of Pₙ (R)

8 0
3 years ago
PLEASE help due today Geometry
irina1246 [14]

\\ \sf\Rrightarrow \dfrac{15}{20}=\dfrac{21}{28}

\\ \sf\Rrightarrow \dfrac{1}{4}=\dfrac{1}{4}

Hence they are similar

#2

  • <A=<H
  • And ratio of sides are same

Hence both triangles are similar by SAS property

#3

\\ \sf\Rrightarrow ∆KDH\sim ∆ABD

8 0
2 years ago
SOMEONE PLEASE HELP DUE TMM
vodka [1.7K]
Yea use a calculator
5 0
3 years ago
Help pls And thanks
hoa [83]

Answer:

I think that 110 would be the correct answer. PLEASE correct if I'm wrong.

Step-by-step explanation:

See, a 90 degree angle is a right angle or like one of the ways you can split a square in half. l

So since that is a little more than a 90 degree angle, I would guess it would be 110.

6 0
2 years ago
Read 2 more answers
Need help asappppppp
Reika [66]

Answer:

press control u on ur google forms quiz than scroll all the way down to the questions and the answer should be right next to them.

4 0
3 years ago
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