a) Find a basis for the range and the rank of the linear transformation T: R3[x] → M2x2(R) given by ao + a1 + 4a2 + az ao + 2a1 + 3az + 2a3 a0 + 3a1 + 2a2 + 2a3 T(ao + a1x + azx² + azx³) = ao + 4a1 + a2 + 3a3 b) Find a basis for the kernel of T and determine the nullity.

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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.