Suppose an nn matrix A has three distinct eivenvalues ,,

. Let B1 be a basis for the eigenspace E

. Let B2 be a basis for the eigenspace E

. Let B3 be a basis for the eigenspace E

Verify that B:=B1B2B3

is linearly independent.

(la-OPT (a points) Suppose an n x n matrixA has three distinct eivenvaiuee A, p, i. Let B] be a basis for the eigenspaee 13;. Let B; be a basis for the eigenspace E\". Let 33 be a basis for the eigenspase E, . Verify that B := Bl U B; U 33 is linearlyI independent. {HmridHint .'Eilimplyr referring to the statement in class to that effect is not enough. The starting idea is as follows: if v; E E4, 12; E E\". and v: E Er. then use results 'em class to showthat ++=f ifand mini}:r if v; = Div; = 03:: (I? Write Bl = (vim; ...,VD, B; = (VE+1.V:+2, ...,v}}. and finallyBg = (VEHJEH, ,V;:l. Conclude that if clvr+ 021:; + +cmv; = [)1 thenc1=c2 = ---=c,,,=[l.} + Drag and drop your images or click to browse