(a) For mod-2 matrix below, (i) calculate the mod-2 product PM, (ii) identify (from the product) which columns corre- sponed to flipped bits, and (iii) decode the intended string. i. ii. 1 1 01 0 1 1 0 1 1 0 [1 1 1 0 1 0 0 0 1 1 1 1 1 1 0 1 1 0 1 0 1 (b) Why does the parity check matrix P detect errors? Suppose your 1-bit message [c] is received as the 3x1 mod-2 matrix M = C2 There are only 8 possibilities for the received vector M. Calculate PM for each of the 8 possibilities, and verify that the error-check conditions from (4) above hold.