Consider the matrices A= bmatrix 1 & 2 3 & 6 bmatrix , B= bmatrix k & -2k 1 & -2 bmatrix

MATHEMATICS · Subjective · AP · AP Precalculus · Functions with Parameters, Vectors, and Matrices · Functions with Parameters, Vectors, and Matrices

Problem

Consider the matrices

A=\begin{bmatrix}1 & 2\\ 3 & 6\end{bmatrix},\qquad B=\begin{bmatrix}k & -2k\\ 1 & -2\end{bmatrix},

where

k

is a real parameter. (a) Find the value(s) of

k

for which

AB

equals the zero matrix of order

2

. (b) For the value of

k

obtained in part (a), write the resultant matrix

B

and verify that it is not the zero matrix. (c) Compute

AB

for this value of

k

to confirm your answer.