Question

Let A = [[1, 2], [1, -2/5]], B = [[7, -3]], and let T: R² → R² be a linear transformation that maps A into B. Find a matrix C such that T(x) = Cx for each x.

Answer 1

To find the transformation matrix C that maps matrix A to matrix B, calculate the determinant of A, find A's inverse if the determinant is non-zero, and multiply B by A's inverse.

Step-by-step explanation:

You're looking for a matrix C such that the linear transformation T(x) = Cx maps matrix A to matrix B. Since T is a linear transformation and A and B are given in their matrix forms, you will first need to determine the matrix that, when multiplied by A, results in B. If we let C be that matrix, the relationship can be described by the matrix equation CA = B. To solve for C, we can multiply both sides of the equation by the inverse of A, provided that A is invertible.

In this case, A is a 2x2 matrix and can be invertible if its determinant is non-zero. First, calculate the determinant of A, and if it's not zero, calculate A-1, the inverse of A. Finally, multiply B by A-1 to obtain the transformation matrix C.

To summarize the steps: calculate the determinant of A, find A-1 if it exists, and then multiply B by A-1 to find C.