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Use the steps below to prove the following relations among
Chapter , Problem 13E(choose chapter or problem)
QUESTION:
Problem 13E
Use the steps below to prove the following relations among the four fundamental subspaces determined by an m × n matrix A.
Questions & Answers
QUESTION:
Problem 13E
Use the steps below to prove the following relations among the four fundamental subspaces determined by an m × n matrix A.
ANSWER:
Solution 13E
Step 1 of 3
Consider a matrix
a)
Suppose is in Row and is in Nul, which implies
This means that each row of A multiplied by is a zero.
So each row of A is orthogonal to in Nul.
By the definition of orthogonal compliment, each row of will be in
As is a subspace, .
Thus, is contained in.