Consider the vector space P, of all polynomials of degree < 1 and consider polynomials p(x)= a,+b, x , q(x)= a,+b, x and inner-product function = a, a,+b, b2 , then the inner-product of p(x)=2+1.7x and q(x)=4.8+3.2x equals: Answer:

Q: Let P3 be the vector space of polynomial functions of degree less than or equal to 3 over the field…

A: Let P3 be the vector space of polynomial functions of degree less than or equal to 3 over the field…

Q: Show that W = {(x1, x2): x1 ≥ 0 and x2 ≥ 0}, with the standard operations, is not a subspace of R2.

A:

Q: Consider the vector space P, of polynomials with real coefficients of degree at most two together…

A:

Q: Problem 1. Consider the vector space P2[x, y](no need to show that it is a vector space) of…

A: Consider the vector space P2[x, y](no need to show that it is a vector space) of polynomials in two…

Q: Find a basis of the subspace of R4 consisting of all vectors of the form ⎡ x1 −8x1+x2…

A: In this we have to find the basis of given vector subspace.

Q: The set of all polynomials of degree 4 under the standard addition and scalar multiplication…

A:

Q: Let P2 be the vector space of all real polynomials of degree at most 2. Let p1, P2, P3 E P2 be given…

A:

Q: The set of all polynomials of degree 6 under the standard addition and scalar multiplication…

A: Polynomials of degree n is a set which is not closed under addition. For example, if n=3, then  x3…

Q: Consider the set P= {1+2x,-1-x+x*,x+x,1+2x+x}. i. Determine if the set P spans the vector space P, ,…

A:

Q: Prove that if W is a subspace of a vector space V and Wt, w2, ... , wn are  in W, then a1Wl +a2W2 +…

A: To Proves: If W is a subspace of a vector space V and w1,w2,...,wn are in W, then…

Q: Use the inner product (5, 9) = [ f(x)g(x) dæ in the vector space P(R) of polynomials to find the…

A:

Q: Consider the vector space V = {p(x) = ao +ajr+azx² | a¡ € R, deg(p(æ)) < 2} of polynomials of degree…

A: Let          V(x)=p(x)=a0+a1x+a2x2 | ai∈ℝ, deg(p(x))≤2 of polynomials of degree less than or equal…

Q: Find a basis {p(x), q(x)} for the vector space {f(x) E P2[x] | f'(-2) = f(1)} where P2[x] is the…

A:

Q: Show if W is a subspace of the vector space X, then W is convex.

A: Definition used: A set K in a vector space V is called convex if and only if  x, y belongs to K,…

Q: Let L = {(x1, x2, x3, X4, X5) E R° | x1 X2 + 2x4 = 0, x2 – 3x4 = 0}. | Prove that L is a subspace of…

A:

Q: Find a basis {p(x), q(x)} for the vector space {f(x) E P2[x] | f'(-8) = f(1)} where P2[x] is the…

A:

Q: Considering the vector space P, of polynomials of order up to 2, calculate the components of the…

A:

Q: In the vector space P, of polynomials of degree at most two, the coordinates of the vector p(x)…

A: Since you have asked multiple question, we will solve the first question for you. If you want any…

Q: Prove that if W is a subspace of a vector space V and w1, w2, . . . , wn are in W, then a1w1 + a2w2…

A:

Q: Find an orthonormal basis for the subspace of Euclidean 3-space below. W = {(x1, x2, x3): x1 + x2 +…

A:

Q: Determine if the set W of vectors (X1 , X2) in R such that x1² + x2 = 0 is a subspace of R?.

A: We have to determine whether W is a subspace of R^2 or not.

Q: V is the linear span of the polynomials a =x' + 2x – 2x + 1, ß=x' + 3x² - x+4, y = 2x +x - 7x – 7…

A:

Q: Produce an example of an element of Co (R, R) which is not an element of the following vector…

A: Correct answer is f(x)= Sin(x) which is infinitely many times continuously differentiable but it is…

Q: and let W the subspace of R" spanned by i and v. Find a basis of W-, the orthogonal complement of W…

A:

Q: Find a basis {p (x), q (x)} for the vector space {f(x) = P3[x] | ƒ' (−1) = ƒ (1)} where P3[x] is the…

A: We have to find p(x) and q(x).

Q: Find a basis {p(x), q(x)} for the vector space {f(x) e P2[x] | f' (7) = f(1)} where P2[x] is the…

A:

Q: Let V be the vector space of polynomials of degree < 2 with real coefficients, endowed with the…

A:

Q: Determine the dimension of the subspace of R consisting of all XeR* such that x1 + 2x, = 0 and X3 –…

A:

Q: Let f(x) = 6, g(x)= 8x + 7 and h(x) = -3x² + 2x + 4. Consider the inner product (p, q) = p(-1)q(-1)+…

A: A

Q: Let V = P2 be the vector space of all polynomials of degree at most 2, with the usual definitions of…

A:

Q: In P2 (polynomials of degree s2), let v =1+x+2x, v, = 3- 2x +x', Determine whether the vector v…

A: Let's find.

Q: In the vector space P,, of polynomials of degree at most two, the coordinates of the vector P(x)…

A:

Q: Let V={a0+a1 x+a2 x2 | a0, a1, a2∈R} be a vector space of polynomial up to degree three, and…

A:

Q: Consider the vector space V, of polynomials of degree less than or equal to 3 that do not have terms…

A:

Q: w that the space V = {(x1, x2, x3) ∈F3

A: To prove that the space V=(x1, x2, x3)∈F3|x1+2x2+2x3=0 forms a vector space.

Q: If W is a subspace of ℝ4 whose dimension is 2 then is any set of 2 vector is a basis for W

A: Answer

Q: The set of all polynomials of degree † under the standard addition and scalar multiplication…

A: Suppose  P7=f(x) | f(x) is a polynomial of degree 7. Then we have to check why this set is not a…

Q: Let P2(R) be the vector space of polynomials over R up to degree 2. Consider {1+x – 2x?, –1 +x+x², 1…

A: Consider the provided question, Given that,  B=1+x-2x2, -1+x+x2, 1-x+x2B'=1-3x+x2, 1-3x-2x2,…

Q: Let V = {ao+a1 x+a2 x² | ao, a1, a2 € R} be a vector space of polynomial up to degree three, and…

A: The vector space of polynomials up to degree three is given by             V=a0+a1x+a2x2a0,a1,a2∈R…

Q: Let H be the set of all vectors of the form 3s . Find a vector v in R3 such that H = Span {v}. Why…

A:

Q: Let V be the vector space of polynomials of degree < 2 with real coefficients, endowed with the…

A:

Q: 5. Consider the vector space P2(R), the set of all polynomial func- tions of degree less than or…

A:

Q: Let T be a linear operator on a finite-dimensional vector space V, and suppose that W is a…

A: Let p(x) be the minimal polynomial of T, hence p(x) annihilates T, i.e.,

Q: 2. Let P2(R) be the vector space of polynomials over R up to degree 2. Consider {1+x - 2a?, -1 +x +…

A: Note: According to bartleby we have to solve only first question please upload the question…

Q: Let V = {ao+ai x+a2 x² | ao, a1, a2 E R} be a vector space of polynomial up to degree three, and…

A: To show that   &lt;p(x),q(x)&gt;=p0q0+p1q1+p2q2 is an inner product on V  and field is of ℝ, we need…

Q: Let f(x) = -1, g(x) = -7x + 2 and h(x) = 5x². %3D Consider the inner product (P, 9) = / P(=)q(=) dz…

A: Given fx=−1, gx=−7x+2 and hx=5x2 And p,q=∫04pxqxdx Gram Schmidt orthogonalization process is  ax=fx…

Q: (b) Consider the vector space V = {p(z) = ao + a1r+ azx² | a; € R, deg(p(x)) < 2} of polynomials of…

A: Consider the vector space V=px=a0+a1x+a2x2: ai∈ℝ, degpx≤2 and W=px∈V:p(1)=0

Q: The set of all polynomials of degree 5 under the standard addition and scalar multiplication…

A: here option (c) is true . because here field is not defined

Q: x=y=z

A:

Linear Algebra

In mathematics, problems can be solved by the arithmetic operators like addition, subtraction, multiplication, and division. In algebra, we represent the numbers by any letter called a variable. If these variables are of degree 1, then it is studied under linear algebra. The first-degree equations involving algebraic expressions are called linear equations. That is, if you represent it by drawing a graph you will get a straight line.