(a) Let F = Z5, V = F^2, W = F^3  as vector spaces over Z5 and let T : V → W be defined by T(x, y) = (x + y, y, x + 2y). Find the matrix representation of T and a basis for both KerT, ImmT. b) Let A, B be similar matrices. If λ is an eigenvalue of A with corresponding eigenvector X. Show λ is an eigenvalue of B and find the corresponding eigenvector.

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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.