Abstract
This chapter reviews the linear transformations of a plane. The chapter discusses a linear transformation relative to a coordinate system. The multiplication of linear transformations of the plane and of square matrices of order two is reviewed. The chapter discusses the addition of matrices, and multiplication of a matrix by a number. The product of linear transformations depends on the order in which these transformations are applied. Two matrices A and B are equal if and only if entries occupying the same position in each matrix are the same, that is, A=B means that the two tables of numbers are identical. A theorem on the determinant of a product of two matrices is also reviewed, which states that the determinant of the product of two matrices is equal to the product of the determinants of the two matrices. The geometric meaning of the determinant of a linear transformation is discussed in the chapter.
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