# Math Help - Linear Algebra Null Spaces and Column Spaces

1. ## Linear Algebra Null Spaces and Column Spaces

Suppose you have a vector space W={a,b,c,d} (W is the column vector a,b,c,d) such that a-3b=4d and 2a=d+5c. How would you go about finding a matrix A such that W=Nul A or W=Col A?

2. ## Re: Linear Algebra Null Spaces and Column Spaces

Hey clintonh0610.

Try modifying the matrix with row operations so that you get your identity (a - 3b = 4d as an example) and once you eliminate two parameters (since you have two independent constraints) reduce it to reduced row echelon form and use the result (plus the rank nullity theorem) to answer the question.