Question

Is it possible that all solutions of a homogeneous system of twelve linear equations in fifteen variables are multiples of one fixed nonzero solution? Discuss. Consider the system as Ax = 0, where A is a 12 x 15 matrix. Choose the correct answer below. O A. No. Since A has 12 pivot positions, rank A = 12. By the Rank Theorem, dim Nul A = 12-rank A = 0. Since Nul A = 0, it is impossible to find a single vector in Nul A that spans Nul A. O B. Yes. Since A has 12 pivot positions, rank A = 12. By the Rank Theorem, dim Nul A = 12-rank A = 0. Thus, all solutions are multiples of one fixed nonzero solution. O C. Yes. Since A has at most 12 pivot positions, rank AS 12. By the Rank Theorem, dim Nul A = 15-rank A23. Since there is at least one free variable in the system, all solutions are multiples of one fixed nonzero solution. OD. No. Since A has at most 12 pivot positions, rank As 12. By the Rank Theorem, dim Nul A = 15-rank A23. Thus, it is impossible to find a single vector in Nul A that spans Nul A.

Answer 1

Answers The Given information is AXo Aisfonder 12x15 12 ARR . .. Rank of A = atmest 12 dim Nillity= 15-12=3 . There are three vaniables XHOJA .: Basis of 3 elements only one element in the basis of Neil CA) is impossible A False option of Correct Nalcas has