Final answer:
The question involves finding the image of a vector under a scalar transformation. The components of the vector in the Cartesian coordinate system are used to describe the vector's position and the transformation applies the scalar to these components.
Step-by-step explanation:
The student question pertains to linear transformations and vector components in a mathematical context. Specifically, a linear transformation t is defined by t(x) = ax, where a is a scalar and x is a vector. The task is to find a vector x and its image under the transformation t.
The vector A can be expressed in terms of its components along the x and y axes, Ax and Ay, forming a right triangle in the Cartesian coordinate system. These components are the projections of vector A onto the respective axes. The scalar components of vector A can be found by subtracting the coordinates of the origin point from the end point of vector A.
Vector A can be represented in component form by A = AxÎ + AyĴ, where Î and Ĵ are unit vectors along the x and y axes, respectively. To find a particular vector x whose image under transformation t needs to be determined, we simply multiply each component of vector x by the scalar a.