(adsbygoogle = window.adsbygoogle || []).push({}); 1. The problem statement, all variables and given/known data

Let A=[{1,3,2,2},{1,1,0,-2},{0,1,1,2}]

i) Find the rank

ii) Viewing A as a linear map from M_{4x1}to M_{3x1}, find a basis for the kernel of A and verify directly that these basis vectors are indeed linearly independent.

2. Relevant equations

None

3. The attempt at a solution

i) is easy enough. Reduce rows to get: A=[{1,3,2,2},{0,1,1,2},{0,0,0,0}] so rank is 2.

ii) I'm not exactly sure of the question here. At first, I thought it was just find the kernel of the matrix and I had some trouble with that. Using the reduced matrix:

x_{1}+ 3x_{2}+ 2x_{3}+ 2x_{4}= 0

and

x_{2}+ x_{3}+ 2x_{4}= 0

but how do I solve this for 4 variables with only 2 equations :/ Any help is appreciated!

**Physics Forums | Science Articles, Homework Help, Discussion**

The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

# Homework Help: Matrix Kernel

**Physics Forums | Science Articles, Homework Help, Discussion**