Let v1 = (4, 6, 7)T , v2 = (0, 1, 1)T , and v3 = (0, 1, 2)T , and let u1, u2, and u3 be the vectors given in Exercise 5. (a) Find the transition matrix from {v1, v2, v3} to {u1, u2, u3}. (b) If x = 2v1 +3v2 4v3, determine the coordinates of x with respect to {u1, u2, u3}.
M303 Section 2.2 Notes- Matrix Inversion 10-10-16 Unlike real (nonzero) numbers, not every matrix has multiplicative inverse × matrix invertible/nonsingular if there exists another × matrix suh that = = o Non-invertible matrix called singular o unique and defined as inverse of , denoted o To check that = , only have to check one equality above o Invertible matrices tell us about invertibility of linear maps (whether is 1-1 and/or onto) Ex. For =[2 5 ]and = [−7 −5 ], show that = . −3 −7 3 2 o = [ 2 5 ][−7 −5 ] −3 −
