Question

Let a, u, and v define t: by t(x) = ax. Find t(u) and t(v).

Answer 1

The function t(x) = ax is a linear transformation applied to vectors. To find t(u) and t(v), multiply the vectors u and v by the scalar a, respectively.

Step-by-step explanation:

The student is dealing with a mathematical concept known as a linear transformation. In the given function, t(x) = ax, a is a scalar, and t is the transformation that multiplies its input by a. To find t(u) and t(v), you simply multiply u and v by a respectively. So you will have:

• t(u) = a × u
• t(v) = a × v

This notation is commonly used in linear algebra to describe how vectors are altered under linear transformations.