Use the properties of linear operations with vectors to show that for any vector a:
->
0a=0
was supposed to look like this:
->
0a=0
Stil not working:
->
0 = 0a
To show that 0a = 0 for any vector a, we can use the properties of linear operations with vectors, specifically the scalar multiplication property.
Let's start by considering the vector a. We know that any vector can be written as a linear combination of its components. Suppose a = (a₁, a₂, ..., aₙ), where a₁, a₂, ..., aₙ are the components of vector a.
Now, let's consider the product 0a. By applying the scalar multiplication property, we can distribute the scalar 0 to each component of the vector a:
0a = (0a₁, 0a₂, ..., 0aₙ)
Since multiplying any scalar by 0 gives us 0, we have:
0a = (0 * a₁, 0 * a₂, ..., 0 * aₙ)
Simplifying further, we get:
0a = (0, 0, ..., 0) = 0
Thus, we have shown that for any vector a, the product of 0 and a is equal to the zero vector, which is denoted as 0.