Construct a matrix whose column space contains (1, 1, 5)

cleritere39

cleritere39

Answered question

2021-12-05

Construct a matrix whose column space contains (1, 1, 5) and (0, 3.1) and whose nullspace contains (1, 1, 2).

Answer & Explanation

Alicia Washington

Alicia Washington

Beginner2021-12-06Added 23 answers

Let us construct matrix A whose column space contains (1, 1, 5) and (0, 3, 1) and whose nullspace contains (1, 1, 2): Easiest way to construct matrix whose colum space contains given vectors is to make those vectors columns of that matrix. Therefore, we have: A=[10a1313a2351a33] We also know that (1,1,2) is in the nullspace of matrix A, which means: [10a1313a2351a33][112]=[000]{a13=12a23=2a33=3 Therefore, we have A=[1012132513] Result: A=[1012132513]

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