Does the multiplication of a scalar and a vector display the commutative property? This property states that the order of multiplication does not matter. So for example, if the multiplication of a scalar s and a vector r is commutative, then sr = rs for all values of s and r.
To determine if the multiplication of a scalar and a vector displays the commutative property, we need to remember the definition of scalar multiplication. In scalar multiplication, a scalar value is multiplied to each component of the vector separately.
Let's consider a scalar s and a vector r.
The scalar multiplication is defined as s * r = (s * r1, s * r2, s * r3, ...), where r1, r2, r3, ... are the components of the vector r.
Now, to check if the multiplication of a scalar and a vector is commutative, we need to compare sr and rs.
For sr, each component of the vector r is multiplied by s. So, sr = (s * r1, s * r2, s * r3, ...).
For rs, we need to multiply each component of the vector r by s. So, rs = (r1 * s, r2 * s, r3 * s, ...).
Since scalar multiplication is a component-wise operation, we can see that sr and rs have the same components in the same order. Hence, the multiplication of a scalar and a vector does display the commutative property.
In summary, for any scalar s and vector r, sr = rs, and the order of multiplication does not matter.