(a) Similar matrices have the same characteristic polynomial. (b) Similar matrices have the same eigenvectors. (c) If A is diagonalizable, then the columns of A are linearly independent. (d) If v is an eigenvector of eigenvalue 5, then –v is eigenvector of eigenvalue –5.

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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.