Question

Linear Algebra

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[1 1 -2 37 1-1 Let A= 0 1 1 1 Lo 0 0 1] [2 a. Is A in row-echelon form, reduced row-echelon form, neither or both? Explain your response in a full sentence. (3 pts) b. Give the solution to the system Ax = b. Format counts. (5 pts) C. What is the dimension of the solution space? Why? (3 pts) d. Is the system consistent for all 3 x 1 matrices b? Why or Why not. Explain in a full sentence (3 pts)

Answer 1

@ Given A= I-2 37 Y- Given matrix A in row-echelon. from, But not in row-reduced echelon form. It reduced row-echelon form, the pivot Column contain's only the pivot element. ② Consider Ax=b. Augmented matrix is ri 1 -2 31-17 0 1 1 1 0 eo

R, R, -R2=) lo-3 ali 101 e é ů, eo R2R2-R3 Sio-3 6-5) Rio R, -AR30i 10-2 Too 012 ► 20, -3303 = -5 xa+*3=-2 x4=2 x₂= a free variable 1 xc,= -5+3a ca= -2-a. . Let

1-5 t + 3 1. Coco So we get loo = - 2 2C2 - x3 لا يع 1 0 m 2 x= x2 Le F-5 X- 22 1-2 tal - >C3 0 رو cu © we know that Ax=b, If oto, then the solution space does not from a subspace since zero vector does not belongs to that collection If b=o, Ax=o, Dimension of solution space is l. @ Yes, because the given matrix A has Romk 3, so for any vector (3*) we can find a vector x such that Ascon vec 107