## Solution for problem 49 Chapter 3.1

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

Linear Algebra with Applications | 4th Edition

Verify that the kernel of a linear transformation is closed under addition and scalar multiplication. (See Theorem 3.1.6.)

**Accepted Solution**

**Step 1 of 3**

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

**Step 2 of 3**

**Step 3 of 3**

Enter your email below to unlock your **verified solution** to:

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