## Description

Given a matrix $A$ and a vector $\mathbf{b}$, we can use the method `.solve_right()` to find a solution to the equation $A\mathbf{x} = \mathbf{b}$. Note that this methods will only provide one solution even if the equation has multiple solutions—if you need to find a solution set, it is better to use the rref method. For example, if

and $\mathbf{b} = (24, 63, 52)$, we can use Sage to solve $A\mathbf{x} = \mathbf{b}$.

## Sage Cell

#### Code

```
A = matrix([[1, 2, 3], [4, 5, 6], [7, 8, -1]])
b = vector([24, 63, 52])
right = A.solve_right(b)
print("right solution =", right)
```

## Options

#### Solving $\mathbf{x}A = \mathbf{b}$

Given a matrix $A$ and a vector $\mathbf{b}$, we can use the method `.solve_left()` to find a solution to the equation and $\mathbf{x}A = \mathbf{b}$.

#### Code

```
A = matrix([[1, 2, 3], [4, 5, 6], [7, 8, -1]])
b = vector([24, 63, 52])
left = A.solve_left(b)
print("left solution =", left)
```

## Tags

CC:

Primary Tags: Linear Algebra: Systems of linear equations

Secondary Tags: Systems of linear equations: Systems with 2 variables, Systems with 3 variables, Systems with 4 or more variables, Matrix-vector forms

## Related Cells

- The RREF of a matrix. Computing the RREF of a matrix.

## Attribute

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Date: 17 Feb 2020 15:50

Submitted by: Zane Corbiere