Construct a matrix whose column space contains (1, 1, 1) and whose nullspace is the line of multiples of (1, 1, 1, 1).

Wribreeminsl

Wribreeminsl

Answered question

2021-08-05

Construct a matrix whose column space contains (1, 1, 1) and whose nullspace is the line of multiples of (1, 1, 1, 1).

Answer & Explanation

lamusesamuset

lamusesamuset

Skilled2021-08-06Added 93 answers

Step 1
Consider the matrix [100101010011]
Step 2
Here, x4 is a free variable and x1,x2,x3 are not. Column space of A contain all combination of vectors [100],[010],[001].
Therefore, it contains vector [111].
Thus, we consider the system [100101010011]=[x1x2x3]=[000]
Step 3
x1x4=0x1=x4
x2x4=0x2=x4
x3x4=0x3=x4
N(A)=x4[1111]
So null space of A consists of all multiples of (1,1,1,1).
A matrix whose column space matrix contains (1,1,1) and whose null space is the line of multiples of (1,1,1,1) is A=[100101010011].

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