a) Let F be the field of complex numbers and let T be the function from F3 into F3 defined by T(x1, X2, X3) = (x, – x2 + 2x3,2x1 + x2, - X1 - 2 x2 + 2x3 ) i. Verify that T is a linear transformation. ii. If (a, b, c) is a vector in F3, what are the conditions on a, b and c that the vector be in the range of T? What is the rank of T? iii. What are the conditions on a, b and c that the vector (a, b,c) be in the null space of T? What is the nullity of T?

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Equations and Inequations

Equations and inequalities describe the relationship between two mathematical expressions.

Linear Functions

A linear function can just be a constant, or it can be the constant multiplied with the variable like x or y. If the variables are of the form, x2, x1/2 or y2 it is not linear. The exponent over the variables should always be 1.