Question

Let A be $3\times 3$ matrix with rank 2. Then AX = 0 has

• A. only the trivial solution X = 0
• B. One independent solution
• C. two independent solutions
• D. three independent solutions

Answer 1

The correct option is B One independent solution

p(A) = 2 and order = 3 and in case of homogeneous system No.of LI solution = order - Rank.
$\therefore$ Number of independent solution = 3-2 =1