15. Let A be the matrix -3 -5 1 -3 1 A 3 -1 -3 -9 3 and let T : R³ → Rª be the linear transformation defined by T(x) = Ax. By referring to the Fundamental Theorem of Linear Algebra we know that %3D a. dim(ker(T)) + dim(Range(T)) = b. Find a basis for ker(T) and a basis for Range(T). Based on the work done in part b we find that dim(ker(T)) = and dim(Range(T)) С.

Let T: R² → R² be a matrix transformation for which: 5 2 -1 7-7( [; D)- E ] 24-7( [] E] Tü = T and = T 2 3 Using the properties of a matrix transformations, determine the following: (a)T(-3ū) = (b)T(7v) = (c)T(-3ū+7v) = 8 1

11. Use matrix multiplication to show that the linear transformation represented by A = [ca as a combination of a reflection across the line y = x and a counterclockwise rotation about the origin by π/2 radians. can be written

Please help with the following: Let T be the linear transformation defined by