Overview:
Matrices, like other numbers, variables, and expressions, can be involved in mathematical operations. The rules are different, as every element of each matrix must be included. Also, only certain types of matrices can be combined.
How Are Matrices Added?
In order to add matrices, both matrices must be of the same dimensions so that corresponding elements can be added. Suppose the matrices to be added were [1 2 3 4] and [5 6 7 8]. In order to add them, each corresponding element would be added, as 1 + 5, 2 + 6, 3 + 7, 4 + 8 or [6 8 10 12].
How Are Matrices Moved?
A matrix can describe the coordinates of a geometric figure as it is drawn on a plane. Suppose triangle ∆ABC has point A at (3, 2), point B at (-3, 0), and point C at (2, -5). A matrix that represents its dimensions would be [3 -3 2 2 0 -5]. If the triangle were moved, or translated, so that it has the same size, shape and direction, 2 units to the right and 2 units down, it would be the same as adding the matrices [3 -3 2 2 0 -5] and [2 2 2 -2 -2 -2] . Using the rule for adding matrices, the new matrix would be[3+2 -3+2 2+2 2-2 0-2 -5-2] or [5 -1 4 0 -2 -7].
How Are Matrices Enlarged?
Matrices are enlarged by multiplying each element of the original matrix by the same number. Suppose triangle ABC, with matrix [3 -3 2 2 0 -5] were to be enlarged so that its perimeter were twice its size. Each element is multiplied by 2, as in 2[3 -3 2 2 0 -5]. The new matrix would be [6 -6 4 4 0 -10].
What Is a Determinant?
A determinant is associated with its square matrix. It can be solved as a single number. Cramer’s rule for evaluating the determinant of a 2 X 2 matrix starts with the matrix itself. Suppose the matrix were [1 2 3 4]. Its determinant would be found by multiplying the 1st and 4th elements (or 1 ∙ 4) and subtracting the product of the 2nd and 3rd elements (2 ∙ 3). In this case, 4 – 6 = -2.
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