 # Linear Algebra Problems

## Transcribed Text

The transformation T IR IR' satisfies Choose one of the following options and justify your answer * T must be linear * T could be linear * T cannot be linear 2 Suppose A is a nxn matrix satisfying AK = 0 for some k>l. Find an inverse for (A-I) 4 Suppose Aisa 3x3 matux such that Ax, for vectors x, X2,X, in RR a if X,IX, X3 are columns of a (3x3) matrix X, / write down the product AX b If the 3 solutions from part (a) are X, (}) X2 = i X3 = Solve Ax= (}) c Find A S Suppose A,B,C are matrices that satisfy : A+ BBT = C which of the following statements must be true? a A is a square matix b A and B have the same size C A B and C have the same number of rows d B has move rows than columns 8 Suppose T is a linear map that maps the point (u,v,w) to (utvtw,Utv,u) Where does T'map the point (XIY,z) ?

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