Let Ŝ be the subspace of C[a, b] spanned by {e², xe², x²e²}. (a) Show that B = {e², xe², x²e²} is a basis of S. (b) Let D: S –→ S be the differentiation operator. Find (D]Bb, the matrix of D with respect to the ordered basis B. Find all the eigenvectors of [D]bb and hence find all the solutions in S of the differential equation df f. dr

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A:

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A: We will use Gram-Schmidt process to form the orthonormal basis of H. According to uk=vk−∑i=1k−1…

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Q: Find the matrix A' for T relative to the basis B'. T: R3 → R3, T(x, y, z) = (y + z, x + z, x − y),…

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A: i just used the definition of matrix of A with respect to basis B'

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Q: Find the matrix A' for T relative to the basis B'. A' = T: R² → R², T(x, y) = (x − 3y, y − x), B' =…

A: Please refer to the solution in next step.

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Q: Suppose A is the matrix for T: R³ → R³ relative to the standard basis. Find the diagonal matrix A'…

A:

Q: Suppose A is the matrix for T: R³ → R³ relative to the standard basis. Find the diagonal matrix A'…

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.