consider the following bilinear form qp defined on IR as follows : p(x, y) x1x2 +3x1Y2 + 3x2Y1+ Y1Y2 where x = ) and y = G). %3D 1) Give the matrix A of o in the canonical basis of IR2. 2) Is the form o symmetric? degenerate? 3) Find the associated quadratic form to p. 4) Find the istotropic cone associated to qp. 5) Is ()1 () with respect to p? 6) Find () .

Q: Estimate the area under the line y= 2x+1 using six rectangles and right endponits over the interval…

A:

Q: 4. Be T: R3 → RS , Linear copy is represented in the standard bases by the matrix: 1 -1 2 1 2 -2 -3…

A:

Q: 26. B = (f1, f2, f3) is a basis for R2[x]. If the change of basis matrix 1 3 from B to Sr, læ] is 1…

A:

Q: 1) Let A = 1 1 0 2 0 03 2-1-1 0 1 4 1 00 0 0 4 0 10 1 0 1 Solve the followings considering the…

A: Apply row operations to get row reduced echelon form of A.

Q: When I was considering what to do with my $10,000 lottery winnings, my broker suggested that I…

A:

Q: Describe all solutions of Ax = 0 in parametric vector form, where A is row equivalent to the given…

A:

Q: Describe all solutions of Ax = 0 in parametric vector form, where A is row equivalent to the given…

A: Given - A is row equivalent to the given matrix 10-2-123001007000019000000 To find - Describe all…

Q: a) Let q(t) = 4t2 + 2t + 9 be an element of P2. Write the coorfinate vector of q(t) relative to…

A: We have to find the followings ; (a) We have to find the coordinate vector of  q(t) = 4t2+2t+9 with…

Q: 2. Suppose a certain system of equations Ar = b has a solution set which can be written in the…

A: The general solution to Ax = b is given by xcomplete = xp + xn, where xn is a generic vector in…

Q: 1. Let u = (2) and v= (2) be non-parallel vectors in the plane. (a) Determine the matrix P that maps…

A: Given: u=sz and v=bc are non-parallel vectors in the plane.   Non-parallel vectors: Non-parallel…

Q: Q. (a) Find an equation of the tangent plane to each surface at the given point. (b) Find symmetric…

A:

Q: 1) Interpolate (by hand) the data x = [-1,0,1] %3D y = [0,1,3] using a) the linear spline basis;

A:

Q: Given [-5 2 3 Q= 2 1 0 3 0 -1] )(10) Find a non-singular matrix P such that P*Q P=D is diagonal.…

A: The given matrix is a) P is a non-singular matrix. We take one non-singular matrix,

Q: 3) a) Are the solutions y₁ = x and y₂ = 3x² −1 linearly dependent or linearly independent? Do they…

A:

Q: a) Explain what it means, by definition, that a polynomial m(x) € P(R) is the minimal poly- nomial…

A: Definition Let  be a A*A matrix. An annihilating polynomial  (i.e., such that m(x)=0) is called a…

Q: Rw = RÔRT %3D

A:

Q: Let T: IR2 > R2 reflection (or orthogonal symmetry) with respect to the line 2x - y = 0. We call…

A: “Since you have posted a question with multiple sub-parts, we will solve the first three sub-parts…

Q: . Consider the set of vectors in R³: It follows that (A) S is a basis for R³ (B) S is linearly…

A:

Q: 1. Describe all solutions of Ax = 0 in parametric vector form, where A is row equivalent to the…

A:

Q: a) Let Vbe a vector space with basis B = {b₁, b₂}. Let T: R² → R² be a linear transofrmation so that…

A: To solve the following

Q: 1. Let R₁ and R₂ be relations on a set A represented by the matrices. 1 0 1 MR₁ = -GD-6D = 1 1 1 and…

A: We are authorized to answer three subparts at a time, since you have not mentioned which part you…

Q: ): Given the matrix 12 3 A =0 14 3 2 3 a) Transform A to the row-echelon form (REF). b) Use…

A:

Q: 2. Consider the quadratic form Q : R° → R, where Q(x1, 22, x3) = –2x – 8x – 18x3+ 8x1x2 + 4x1x3 +…

A: The given quadratic form is Q(x1,x2,x3)=-2x12-8x22-18x32+8x1x2+4x1x3+4x2x3 The quadratic homogenous…

Q: Describe all solutions of Ax=0 in parametric vector form, where A is row equivalent to the given…

A:

Q: (g) Consider the following matrix A = a) A = QAQT possible? b) A non-diagonalizable. c) A singular?…

A: Please see the below pictures for detailed solution.

Q: Consider the orthogonal basis B = {e = (2, 2, –1); f = (2, –1, 2); g = (–1, 2, 2)}, determines the…

A: Given that B= {(2,2,-1),(2,-1,2),(-1,2,2)}. We need to find the coordinates of the vector (1,-1,0)…

Q: Given the ordered basis B = {p1 =1– 1, P2 = 4 – 7x find [p]B, the coordinates of p = -7+ 10x with…

A: Follow next step

Q: 6. Verify that S is an orthogonal basis for R³. Use this to write u as a linear combination of the…

A:

Q: 9. Find a basis for the hyperplane a where a-(2, 1, -3).

A: Any two linearly independent vectors which are orthogonal to the given a are forms a orthogonal…

Q: Let T be the reflection about the line -2x + ly = 0 and T, be the reflection about the line 2x +…

A: Every matrix has 2 attributes, rows and columns, if a matrix A is represented as Amxn, then m…

Q: Describe all solutions of Ax = 0 in parametric vector form, where A is row equivalent to the given…

A:

Q: Let V = R³, let B = {bi,b2, b3} be the basis of R³ defined below, and let F(7) = Aī. %3D %3D 1 1 A =…

A: Given that V=ℝ3, let B=b¯1, b¯2, b¯3 be the basis of ℝ3 defined below, and let Fx¯=Ax¯.…

Q: Let A = 2 1 29 2 36 and let W= COICA). Find on orthonormal basis for W. . Find a basis of W. Set up…

A: (a) Given: A matrix A=2129-1236 and let W=Col(A). To find:  Find orthonormal basis for W. Find a…

Q: Describe all solutions of Ax = 0 in parametric vector form, where A is row equivalent to the given…

A: The given row equivalent matrix is, 14-4901-48 We have to find the solution of this system.

Q: Let W be the plane with the equation 3x-y+ 7 = 0. Find the standard matrix P for the orthogonal…

A: