Determine whether the statements that follow are true or false, and justify your answer.There exists a 5 x 5 matrix A of rank 4 such that the system AJc = 0 has only the solution x = 0.

Data Analysis Formulas Midterm 1 2 2 n(xi−´) Sample Variance- s =∑ (n−1) i=1 n 2 (xi−´ ) Sample Standard Deviation- s= √i=1(n−1) c P(E) (Independent event)= 1-P(E ) P(A/B)= P(A∩B) Conditional Probability= P(B) P(B)+P(B )=1 Probability= P(A/B)P(B)+P(A/B )P(B ) Probability= P(A∩B) Independence= = P(A)*P(B)