For the matrices (a) find k such that Nul A

arneguet9k

arneguet9k

Answered question

2021-11-17

For the matrices (a) find k such that Nul A is a subspace of Rk, and (b) find k such that Col A is a subspace of Rk
A=[4526011010]

Answer & Explanation

Feas1981

Feas1981

Beginner2021-11-18Added 16 answers

a) In order to find Nul A, we must solve
Ax=0
Since A is 2×5 matrix, it can multyplied from left only by vector with 5 rows. That means x is in R5, i.e. k=5
b) As we saw in part a) xR5, so we know
Col A={y:y=Ax  for some  xR5}
So we have a multiplication of 2×5 matrix A and 5×1 vector x. From definition of matrix muplication, y is 2×1 vector, i.e k=2
Result: a) 5, b) 2

Do you have a similar question?

Recalculate according to your conditions!

Ask your question.
Get an expert answer.

Let our experts help you. Answer in as fast as 15 minutes.

Didn't find what you were looking for?