Knowen - Definition of constant vector of a linear system

Created almost 9 years ago, updated 5 months ago

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Definition: Constant Vector

The constant vector of a linear system is the m × 1 column vector containing the right-hand side values (the constants) from each equation.

For the system Ax = b, the constant vector b is:

b = [b₁]
    [b₂]
    [...]
    [bₘ]

Example: For the system:

2x + y - z = 8
-3x - y + 2z = -11
-2x + y + 2z = -3

The constant vector is:

b = [ 8]
    [-11]
    [ -3]

The constant vector determines whether the system is homogeneous (b = 0) or non-homogeneous (b ≠ 0).

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Terminology

**Definition: Constant Vector**

The constant vector of a linear system is the `m × 1` column vector containing the right-hand side values (the constants) from each equation.

For the system `Ax = b`, the constant vector `b` is:
```
b = [b₁]
    [b₂]
    [...]
    [bₘ]
```

**Example:** For the system:
```
2x + y - z = 8
-3x - y + 2z = -11
-2x + y + 2z = -3
```

The constant vector is:
```
b = [ 8]
    [-11]
    [ -3]
```

The constant vector determines whether the system is homogeneous (`b = 0`) or non-homogeneous (`b ≠ 0`).

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