# How do you know if a matrix is inconsistent or consistent?

**whether**or not an augmented

**matrix**is

**consistent**is by first row reducing it.

**If**, after row reducing, you see something like this: the

**matrix is inconsistent**. Notice the last row.

Simply so, what does it mean for a matrix to be inconsistent?

**Definition** 1.5. 2 A system of linear equations **is** called **inconsistent** if it has no solutions. A system which has a solution **is** called **consistent**. If a system **is inconsistent**, a REF obtained from its augmented **matrix** will include a row of.

**Cramer's Rule**for a 2×2 System (with Two Variables)

**Cramer's Rule**is another method that can solve systems of linear equations using determinants. In terms of notations, a

**matrix**is an array of numbers enclosed by square brackets while

**determinant**is an array of numbers enclosed by two vertical bars.

In this manner, what does infinitely many solutions look like?

The first **is** when we have **what is** called **infinite solutions**. This happens when all numbers **are solutions**. This situation means that there **is** no one **solution**. The equation 2x + 3 = x + x + 3 **is** an example of an equation that has an **infinite** number of **solutions**.

A **matrix** is in reduced **row**-echelon form when all of the conditions of **row**-echelon form are met and all elements above, as well as below, the leading ones are zero. If there is a **row** of all **zeros**, then it is at the bottom of the **matrix**. All elements above and below a leading one are zero.