Describe the four subspaces of R³ associated with the matrices: [010] 1 1 0 A 0 0 1 (I+A) 0 1 1 001 [000] and

and Consider the subspaces X - U = span{[153], [-4 3-1]} W = span{ [-4_2_-4],[-18 0 -16]} of V = R ¹x3. Find a matrix X EV such that U W = span{X}.

Let A be an n x n matrix, let S = (ü, ü, u) be a set of non-zero vectors in R", and let U be a subspace of R" of dimension at least 1. Look at the expressions and phrases that follow. Select the ones that DO NOT make sense, because they either equate two different "types" of thing that can't be equal, use nonsensical notation, or try to perform an operation that is not defined. (For the computer programmers reading this, the question is essentially "find the type errors".) Warning: To clarify, you're not being asked which ones are true. You're being asked to identify which equations don't make sense. From the 11 choices, select all that apply "a basis of 5" "the solutions of the system of equations" im(A) (R" Ay for some FR") "the span of A" im(A) - (A#-5) "S spans U "the solutions of the matrix" im(A) {ER: Af=ÿ) null(A) = {A=0} 1 null(4)-(ER": Až=6) "U spans S"

Every subspace W of R" can be written as an eigenspace of some n X n matrix. true false