Activity in China’s factory and services sectors fell last month to its lowest level since the aftermath of the global financial crisis, the latest signal of a deepening economic slowdown that prompted the central bank to inject cash into the banking system on Monday.  China’s official manufacturing purchasing managers’ index fell to 49 in February from 49.8 in January, equalling its weakest since February 2009 and the seventh straight month of decline. The National Bureau of Statistics, which released the measure, said this was partly due to seasonal effects of the lunar new year holiday, when many factories shut down for extended periods to allow workers to travel to distant hometowns to spend time with their families.  The official services sector PMI, which had previously held up better than the manufacturing index in China’s economic slowdown, also slipped last month to 52.7, its weakest level since December 2008. Meanwhile, the privately sponsored Caixin PMI came in weak, with an accompanying commentary noting a drop in workforce levels.  “Staff numbers declined at the sharpest rate since January 2009 during February,” said He Fan of Caixin Insight group. “Companies that recorded lower headcounts widely commented on company downsizing policies as part of cost-cutting initiatives, along with the non-replacement of voluntary leavers.”