Problem 4 Find the matrix MDB of T: P2 → R² with T(a + bx + cx²) = (a+c, 2b) corresponding to the bases B = {1, x, x²} and D {(1, 0), (1, 1)}, respectively, and use it to compute CDT(v)], and hence T(v) for v = a + bx + cx². =

Q: Let A be a 5 x 5 matrix with det(A) = -10. 1. If the matrix B is obtained from A by adding 4 times…

A:

Q: c1x1(a) + c2x2(a)+ . . . +cnxn(a) = x(a). Let X (t) be the n x n matrix with column vectors x1, x2,…

A: Given : Xt be any  matrix of n×n           : c be column with component c1 ,c2 , . . .  . . .  ,cn…

Q: 2. Write the following in vector/matrix notation, specifying all components of the matrices. If it…

A:

Q: Find an orthogonal matrix P that orthogonally reduces the quadratic form Q(x) = x" Ax sa} + 3.x3 +…

A:

Q: Which of the following is a topology on X = {1,2,3,4} T= {4. {1}.{2}. {1,2},{3}} T = {4.X. {1}.{2}}…

A:

Q: Let B=(b₁,b₂), C={C₁,C₂), be bases for R² b₁ = (-1,2), b₂ = (1, -1), C₁=(1,2), C₂ = (1,1) Find the…

A:

Q: Consider matrix A = (₁ (2) Answer: and vectors x = (-²2) and y = (¹). Calculate matrix B= (A - AT)2…

A:

Q: Suppose (B-C)D=0, where B and C are mxn matrices and D is invertible. Show that B = C.

A: The given matrix equation is B-CD=0 B and C are the matrices of the order m×n while D is the…

Q: Find the matrix of T(ax² +bx +c) =(a-b)x² +2cx with respect to the basis {x*,x,1} of P,. Use the…

A:

Q: let Q(x)= x12 -8x1x2 -5x22 , then matrix A of the quadratic from is A=?

A: Explanation is given below..

Q: Suppose that A and B are invertible 2 x 2 matrices such that det(AT) = 2 and det(B) = -2. Let x ER…

A:

Q: Rewrite as a matrix-vector product: Зх + 4у — z + w%3D 12 -x + 2y – z +w = 9 2х — Зу + 2z — 4w %3D -…

A: Here we have to rewrite as a matrix-vector product:  3x+4y-z+w=12-x+2y-z+w=92x-3y+2z-4w=-3

Q: 6 and u = 5 Write y as the sum of two orthogonal vectors, one in Span {u} and one orthogonal to u.…

A: A vector has 2 components, magnitude and direction which is represented by cos and sin angles. A…

Q: 6. Find the distance between the matrices A and B, p(A, B), using the ||- ||2 for the matrix -[:] -1…

A:

Q: Find the change of basis matrix from B1 to B2. -1 2

A:

Q: The commutator [X. Y] of two matrices is defined by the equation [X. Y] = XY YX. Two anticommuting…

A: The matrices  A, B satifies the property A2=I, B2=I and A, B=2iC. The matrices A, B are…

Q: -) Let A, B be nx n symmetric matrices such that XTAX = X™BX for all %3D column vectors X e R". Show…

A: note : as per our guidelines we are supposed to answer only one question. Kindly repost other…

Q: b) Evaluate det[(2A)-1 (3A")], where A is any invertible (2 x 2) matrix.

A:

Q: (4) Let A be an invertible matrix. Prove that if A = Q¸R1 decompositions of A and if the diagonal…

A:

Q: Consider the bases B1 = {(1,2), (- 3,0)} and B2 = {(3,2), (- 1, –2)} of R. The input to "(2.1)' of…

A: Consider the given vectors. B1=1,2,-3,0B2=3,2,-1,-2 Express the vectors in linear combination.…

Q: 2. Find the coordinate matrix of 7 = ³- {)-(-9)} B = 2 0 0 6 2 relative to the basis

A:

Q: Consider the following matrix: 1 2 3 0 -3 A-3 6 -9 09 -2 5-9 -29 Give a basis for each of im(A) and…

A:

Q: Suppose B and D are the following two bases for P2: B=|4x²-4x-2, ²-4x−2, 3x²-x, −3x−3] D= [-3x−3,…

A:

Q: Give an example of a 2 x 3 matrix A that is in RREF and whose solutions to 2 -(-) 4 Ax = 0 is…

A: Introduction: Systems of linear equations can be solved using a type of matrix called reduced row…

Q: 9. Given the bases B = {1+2t, 2+t} and C = {1-t, 2-3t) of P₁. Find the change of coordinates matrix…

A: As per the question we are given two different bases B, C of same polynomial space {1, t} And we…

Q: Consider the matrix B given by 0 0 0 B = 1 0 0 0 1 0 Show that B3 = 0. Also, compute for the product…

A:

Q: X= 3 -2 0 0 + -2 1 1 0 1 2 S+ t 0 1 Find a Basis for Column B of this Matrix

A: The row space (Row B) of a matrix is the set of all possible linear combinations of its row vectors.…

Q: Let y = and u= 3 Write y as the sum of two orthogonal vectors, one in Span {u} and one orthogonal to…

A:

Q: If A is an nxn invertible matrix, then Select one: -1 a. A"= det(A)/adj(A) -1 b. A"=…

A:

Q: 2. Find a matrix that projects onto the line / 2x - 5y = 0 and find the projection of 6= (1, -2)…

A:

Q: If the matrices A and B are conformable for sum A+B the product AB then prove that (A+B)" = A" +B"…

A: Prove that. (a).A+BT=AT+BT(b).ABT=BTAT