Question

A is a 3 times 3 matrix with three pivot positions.

Answer 1

Answer:

The following are the answer:

In option a  "No".

In option b  "Yes".

Step-by-step explanation:

In choice a:

Ax = 0 has no nontrivial solution. A would be the three-pivot matrix, it may assume, that the function has no free variable, and only if the function has had at least one free factor are their nontrivial formulas for the equations of the form Ax=0.  

It implies that since A is a 3x3 matrix, has no free variables so that it has no non-trivial choices, and Ax = 0.

In choice b:

we assume that every potential has at least one solution that is Ax=b . If A does have a three-pivot matrix, It will be a pivot element for each row and column, and for each possible b∈ R³, Ax = b has at least one solution.