Let P be the vector space of polynomials of degree at most 2. Let L: P → P2 be the linear transformation given by L(p(t)) = 1p"(t) + lp'(t) + 1p(t). Let E = (e1, e2, e3) be the basis of P² given by e1(t) = 1, e2(t) = t, e3(t) = t². Find the coordinate matrix Lɛɛ of L relative to the ordered bases E.

Q: Let T be a linear transformation from R2 into R² such that 7(1, 0) = (1, 1) and 7(0, 1) = (-1, 1).…

A:

Q: Find the change-of-coordinate matrix P from B to C and P from C to B for the bases B = {1,t,t^2} and…

A: Let U={u1,u2,⋯,un} and V={v1,v2,⋯,vn} are two bases of a vector space W.The identity map I:W→W…

Q: Let U = p E 4 (R): 1 -1 p = 0}. Find a basis of U.

A:

Q: a) From the vector space of polynomials of degree at most 3 to itself the following linear…

A:

Q: Find the matrix A' for T relative to the basis B'. T: R2 → R2, T(x, y) = (x + y, 5y), B' = {(-4, 1),…

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.