7. Find the standard matrix for the linear transformation T. T:R²→R², T maps ei to e̟ +4e2 but leaves e2 unchanged.

Let T be the linear transformation defined by T(x, y) = (-9y,4x + y, 5y – 8x, 2y – 7x). Find its associated matrix A. A =

5. Consider a linear transformation T: R2 → R2 which reflects a vector about the line y=-x, and dilates the reflected vector by a factor of 2. Find the standard matrix for the linear transformation.

assume that T is a linear transformation. Find a Standard matrix of T. T: IR² →IR" 8) where A T(e₁) = (5,1,5,1) T(e₂) = (-3₁7,0,0) ? e₁ = (1,0) € 2 = (0₁1) (integer or decimal)