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Determine whether each of the following is a subspace of the parent vector space.The set of polynomials of the form ax + Bx-a, where a,B are scalars.2а.-xXThe set of 2 x 2 matrices of the form1where x is a scalar.b.X

Question
Determine whether each of the following is a subspace of the parent vector space.
The set of polynomials of the form ax + Bx-a, where a,B are scalars.
2
а.
-x
X
The set of 2 x 2 matrices of the form
1
where x is a scalar.
b.
X
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Determine whether each of the following is a subspace of the parent vector space. The set of polynomials of the form ax + Bx-a, where a,B are scalars. 2 а. -x X The set of 2 x 2 matrices of the form 1 where x is a scalar. b. X

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Step 1

To determine whether the given subsets are subspaces

Step 2

(a) In this case W is a subspace of the parent vector space V, ...

a) Let W = {ax + Bx-a:a,ß scalars
V = the vector space of all polynomials
Let f axBx-a,g=rx +ôx-yeW;
Now, fg (a)+(B+S)-(a+y) E W
and cf caxcx-ca e V
help_outline

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a) Let W = {ax + Bx-a:a,ß scalars V = the vector space of all polynomials Let f axBx-a,g=rx +ôx-yeW; Now, fg (a)+(B+S)-(a+y) E W and cf caxcx-ca e V

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