Linear AlgebraShow your calculations1. If possible, write -15 - 2x + 7x^2 as a linear combination of -2 - x + x^2, x^2 - 2 and 5 + x -2x^2. Otherwise, enter DNE in all answer blanks.-15 - 2x + 7x^2 = [answer blank] (-2 - x + x^2) + [answer blank] (x^2 - 2) + [answer blank] (5 + x -2x^2).2. Determine whether each set {p1,p2} is linearly independent set in P3. Type "yes" or "no" for each answer.The polynomials p1(t) = 1 + t^2 and p2(t) = 1 - t^2 The polynomials p1(t) = 2t + t^2 and p2(t) = 1 + t The polynomials p1(t) = 2t - 4t^2 and p2(t) = 6t^2 - 3t3. Determine if each of the following sets is a subspace of Pn, for an appropriate value of n. Type "yes" or "no" for each answer.Let W1 be the set of all polynomials of the form p(t) = at^2, where a is in RLet W2 be the set of all polynomials of the form p(t) = t^2 + a, where a is in RLet W3 be the set of all polynomials of the form p(t) = at^2 + at, where a is in R
Linear Algebra
Show your calculations
1. If possible, write -15 - 2x + 7x^2 as a linear combination of -2 - x + x^2, x^2 - 2 and
5 + x -2x^2. Otherwise, enter DNE in all answer blanks.
-15 - 2x + 7x^2 = [answer blank] (-2 - x + x^2) + [answer blank] (x^2 - 2) + [answer blank] (5 + x -2x^2).
2. Determine whether each set {p1,p2} is linearly independent set in P3. Type "yes" or "no" for each answer.
The polynomials p1(t) = 1 + t^2 and p2(t) = 1 - t^2
The polynomials p1(t) = 2t + t^2 and p2(t) = 1 + t
The polynomials p1(t) = 2t - 4t^2 and p2(t) = 6t^2 - 3t
3. Determine if each of the following sets is a subspace of Pn, for an appropriate value of n. Type "yes" or "no" for each answer.
Let W1 be the set of all polynomials of the form p(t) = at^2, where a is in R
Let W2 be the set of all polynomials of the form p(t) = t^2 + a, where a is in R
Let W3 be the set of all polynomials of the form p(t) = at^2 + at, where a is in R
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