Let E= {e,, e2, e3} be the standard basis for R°, B= (b, , b2, b3} be a basis for a vector space V, and T:R° → V be a linear transformation with the property that (x1, X2, ×3) = (x3 - ×2) b, - (×1 + X3) b2 * (x1 - X2) b3. a. Compute T(e,), T(@2), and T(@3). p. Compute [T(e1)]B• [T(@2)]8• and [T(®3)]B• . Find the matrix for T relative to E and B. .. a. T(e,) =], T(e2) =D, and T(e3) = [ ["(•) ]==D•["(*2) ]e-0, and [T(*3) ]e =D c. The matrix for T relative to E and B is.

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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.