Consider a nonzero 3 x 3 matrix A such that A2 = 0. Show that the image of A is a
Chapter 7, Problem 58(choose chapter or problem)
Consider a nonzero 3 x 3 matrix A such that A2 = 0. Show that the image of A is a subspace of the kernel of A. Find the dimensions of the image and kernel of A. Pick a nonzero vector 5i in the image of A, and write Vl = A^2 for some V2 in R3. Let 1)3 be a vector in the kernel of A that fails to be a scalar multiple of 5i. Show that s23 = (v\, V 2,1 )3) is a basis of R3. Find the matrix B of the linear transformation T(x) = Ax with respect to basis 33.
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