Find the Pre-Image A=[[1],[5],[6]] , x=[[1],[-2],[8]]

Problem

A=[[1],[5],[6]],x=[[1],[−2],[8]]

Solution

1. Identify the task as finding the pre-image of a vector under a transformation. However, the notation provided defines A as a 3×1 column vector and x as a 3×1 column vector. In linear algebra, the image of a vector x under a matrix A is typically defined by the matrix-vector product A*x

2. Check for compatibility. For the product A*x to be defined, the number of columns in A must match the number of rows in x Here, A is a 3×1 matrix and x is a 3×1 matrix.

3. Conclude that the operation A*x is undefined because a 3×1 matrix cannot be multiplied by a 3×1 matrix. If the task implies the dot product A⋅x the calculation would be (1)*(1)+(5)*(−2)+(6)*(8)

4. Calculate the dot product.

1−10+48=39

Final Answer

A⋅x=39

Want more problems? Check here!