Let be the set of all symmetric matrices all whose entries are either 0 or 1

MATHEMATICS · Multi-part · AP · AP Precalculus · Functions with Parameters, Vectors, and Matrices · Functions with Parameters, Vectors, and Matrices

Problem

Let

A

be the set of all

3 \times 3

symmetric matrices all whose entries are either 0 or 1. Five of these entries are 1 and four of them are 0. (1) The number of matrices in

A

is (A) 12 (B) 6 (C) 9 (D) 3. (2) The number of elements in

A

for which the system of linear equations

A \begin{bmatrix} x \\ y \\ z \end{bmatrix} = \begin{bmatrix} 1 \\ 0 \\ 0 \end{bmatrix}

has a unique solution, is (A) Less than 4 (B) At least 4 but less than 7 (C) At least 7 but less than 10 (D) At least 10.