# What does it mean when Ax B has no solution?

## What does it mean when Ax B has no solution?

It just means that there are some vectors b for which Ax = b does not have a solution. A solution x is non-trivial is x = 0. • The homogeneous system Ax = 0 has a non-trivial solution if and only if the equation has at least one free variable (or equivalently, if and only if A has a column with no pivots).

## How do you know if an equality has no solution?

Isolate the absolute value expression on the left side of the inequality. If the number on the other side of the inequality sign is negative, your equation either has no solution or all real numbers as solutions.

What math has no solution?

No solution would mean that there is no answer to the equation. It is impossible for the equation to be true no matter what value we assign to the variable. Infinite solutions would mean that any value for the variable would make the equation true. No Solution Equations.

### How do you prove a system of equations has no solution?

When two equations have the same slope but different y-axis, they are parallel. Since there are no intersection points, the system has no solutions.

### Is there any vector B for which the equation Ax B has no solution explain?

This means that if Ax = b has solutions, then the sum of the entries in b must be zero. Equivalently, if b is any vector whose sum of entries is nonzero, then Ax = b has no solutions.

What is Ax B when does Ax B has a unique solution?

The system AX = B has a unique solution provided dim(N(A)) = 0. Since, by the rank theorem, rank(A) + dim(N(A)) = n (recall that n is the number of columns of A), the system AX = B has a unique solution if and only if rank(A) = n.

#### What circumstances would cause a system of inequalities to have no solution?

When two inequalities have parallel lines and the shaded areas do not overlap (i.e., the opposite areas are shaded), then the system has no solution. This means that there is no coordinate point that makes both inequalities true.

#### What equation has infinite solutions?

The equation 2x + 3 = x + x + 3 is an example of an equation that has an infinite number of solutions.

How do you make a no solution equation?

To create a no solution equation, we can need to create a mathematical statement that is always false. To do this, we need the variables on both sides of the equation to cancel each other out and have the remaining values to not be equal.

## What are the conditions for no solution?

If (a1/a2) = (b1/b2) ≠ (c1/c2), then there will be no solution. This type of system of equations is called an inconsistent pair of linear equations. If we plot the graph, the lines will be parallel and system of equations have no solution.

## Which statement is true about the system Ax B have at least one solution for every B?

Answers to Quizlet 1-5

Question 6. A is a 3×3 matrix with 3 pivot positions. Select all the statements which must be true for this A. Ax = 0 has a nontrivial solution. False
Ax = b has at least one solution for every possible b. True