Matrix: Subtraction

Matrix: Subtaction

Return to Roadmap 3

We can use the GNRNDM program with the key values -8632501809 3434242424 and 0 to generate the matrices:

The calculator used to obtain the images below was a TI 84 Plus C running the 4.0 operating system and it was in the MATHPRINT display mode. These images merely reflect generating the matrices.

We approach matrix subtraction in the same way that we approach numeric subtraction. That is, in a specific case, say 5-3 we change that to 5 + ^–3; we change the subtraction problem into an addition problem. In general, for numbers a and b, the problem a - b becomes a + ^–b. Also, we understand that for numbers, in geneeral, we have that ^–b = (^–1) * b. Our calculator does this same thing for matrix subtraction. That is, we interpret [A] – [B] to be the same thing as [A] + ^–[B] which is the same as [A] + (^–1)*[B]. In effect, we subtract matrices by subtrracting, in the proper order, the correspondingelements of the two matrices. An example or two should make this more concrete.

Figure 01
Figure 02	Then we can look at [A]–[C] and at [C]–[A], which give opposite results just as `7 – 3 = 4` but `3 – 7 = ^–4`.
Figure 03	Just to show that our disussion above holds, we can take `^&ndash1` times [B], store the result in [F] and then have the calculator find [A]+[F] to get the same result that we had back in Figure 01 with [A]ndash;[B].
Figure 04	We finish this page with a small demonstration of subtracting two `3 x 4` matrices as in [D]–[E].