(a) Define a zero (null) matrix. (b) Two non-zero matrices are given below: A=…
MATHEMATICS · Subjective · AP · AP Precalculus · Functions with Parameters, Vectors, and Matrices · Functions with Parameters, Vectors, and Matrices
Problem
(a) Define a zero (null) matrix.
(b) Two non-zero matrices are given below:
A=[12−1−2],B=[1111].
(i) Show that AB is the zero matrix of order 2.
(ii) Verify explicitly that neither A nor B is the zero matrix.
(c) Explain, without performing any further calculation, why the existence of such matrices does not contradict the fact that, for real numbers, a product equal to zero implies at least one factor is zero.