Can someone help me solve these two questions regarding matrices? I am asked to find the general solution for the augmented matrix in the first question, and the description for matrix b in the second question, I included an image to make it clearer. I attempted to solve them but I'm not sure of the answer.

The first question

The augmented matrix is given for a system of equations. If the system is consistent, find the general solution. Otherwise state that there is no solution.

(This is one matrix )

A= [1 -5 -1]

[0 0 7]

a)x₁= -1 + 5x₂

x₂is free

b)(-1, 7)

c)x₁= -1 + 5x₂

x₂= 7

x₃is free

d)No solution

the second question

Let

A= [1 -3 2 ]

[-2 5 -1]

[3 -4 5]

B= [ b₁]

[b₂]

[b₃]

(These are two matrices a and b)

Determine if the equation Ax = b is consistent for all possible b₁, b₂, b₃. If the equation is not consistent for all possible b₁, b₂, b₃, give a description of the set of allbfor which the equation is consistent (i.e., a condition which must be satisfied byb₁, b₂, b₃₎

a)Equation is consistent for all possible b₁, b₂, b₃.

b)Equation is consistent for all b₁, b₂, b₃satisfying 7b₁+ 5b₂+ b₃= 0.

c)Equation is consistent for all b₁, b₂, b₃satisfying -3b₁+ b₃= 0.

d)Equation is consistent for all b₁, b₂, b₃satisfying 2b₁+ b₂= 0.