Consider the matrix A= pmatrix 2 & 4 & 2 1 & 2 & 1 3 & 6 & 3 pmatrix

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

Problem

Consider the matrix

A=\begin{pmatrix}2 & 4 & 2\\1 & 2 & 1\\3 & 6 & 3\end{pmatrix}.

(i) Calculate

|A|

. (ii) On the basis of the value obtained in part (i), decide whether

A

is invertible and justify your answer. (iii) If a matrix

B

were to satisfy

AB=I_3

, explain why such a matrix cannot exist for the given

A