If a and b are integers, not both of which are zero, prove that gcd(2a - 3b, 4a - 5b)divides b; hence, gcd(2a + 3, 4a + 5) = 1.

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 −