one, infinite or no solutions. I am mainly confused about how the reduced row ec

Question

one, infinite or no solutions.

I am mainly confused about how the reduced row echelon form, helps you determine the number of solutions.

Thanks in advance.

Explanation / Answer

[ 0 2 1 ] A = [ 0 3 2 ] [ 2 0 0 ] [ -1 ] B = [ 0 ] [ 2 ] (A | B)= [ 0 2 1 -1 ] [ 0 3 2 0 ] [ 2 0 0 2 ] interchange R3 and R1 [ 2 0 0 2 ] [ 0 3 2 0 ] [ 0 2 1 -1 ] R3 -> 3*R3 - 2*R2 [ 2 0 0 2 ] [ 0 3 2 0 ] [ 0 0 1 -3 ] it is in row echelon form and rank(A | B) = number of non-zero rows in the row echelon form of the matrix =3 and rank(A) = 3 here, rank(A | B)=rank(A)=3 only one solution exist if, 1) rank(A | B)=rank(A)= n where n is number of rows in the given matrix. Then the matrix contains one unique solution. 2) rank(A | B)=rank(A)

Related Questions

Navigate

• Browse (All)
• Browse O
• Subjects

---

---

Integrity-first tutoring: explanations and feedback only — we do not complete graded work. Learn more.