Verify that the kernel of a linear transformation is closed under addition and scalar

Sonny Chauhan RPI Abstract Algebra notes (week 1): Well ordering Principle: Every nonempty set of positive integers contains a smallest number, member. Divisor: is when a number is divisible by another number. When we divide the numbers we get remainder 0. For example a nonzero integer t is a divisor of the integer s if t is divisible by s. That means there exists an integer u such that s=tu. We write t|s also known as (“t divides s”). Division Algorithm: Let b>0 and a and b be integers. There has to exist integers q and r where r is greater than or equal to 0 and less than b such that a=bq+r. In this case a is the dividend, b is the divisor, q is the quotient and R is the remainder. For example: 345/8= 43 remainder 1. Thus by the division algorith