Question: Problem 3. (8 POINTS) WHICH STATEMENT IS ALWAYS CORRECT? A. FOR AN m X n MATRIX A IF AX = 0 HAS A NONZERO SOLUTION,

Problem 3. (8 POINTS) WHICH STATEMENT IS ALWAYS CORRECT? A. FOR AN m X n MATRIX A IF AX = 0 HAS A NONZERO SOLUTION, THEN THE RANK OF A IS n. B. EACH SYMMETRIC MATRIX IS NONSINGULAR. C. FOR A SQUARE MATRIX, A, IF A2 = AA = 0 THEN A MUST BE THE ZERO MATRIX: A = 0. D. IF A MATRIX A IS A SYMMETRIC MATRIX, THEN THERE EXISTS A NONSINGULAR MATRIX, Q, SUCH THAT QAQT IS A DIAGONAL MATRIX. E. A LINEAR SYSTEM OF FOUR EQUATIONS WITH THREE UNKOWNS IS ALWAYS INCON- SISTENT

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