Question: linear transformation

Let A be an m×n matrix. The kernel of A  is the set of vectors

ker(A)={x:Ax=0} ,

which is a vector space.

The dimension of ker(A)  is called the nullity of A, denoted by nullity(A) .

   (a)  Find the nullity of the matrix 

v1:=<136, 40, 124, -94>

v2:=<-74, -54, 150, 99>

v3:=<-104, 68, 196, -134>

v4:=<-38, -142, -108, 280>

v5:=<342, -326, -634, 635>

A:=<v1|v2|v3|v4|v5>

and enter in the box below.

nullity(A)=     

      b) For the matrix A in (a), select all the statements below which are true.

 (1)  <71, -37, 44, 73> is in ker(A)

 (2) <-1,1,2,-2,1> is in ker(A)

 (3) <0,0,0,0> is in ker(A)

 (4) <0,0,0,0,0> is in ker(A)

 (5) ker(A) is a subspace of R^5

 (6) ker(A) is a subspace of R^4

 (7) <95,-72,-85,-12> is in ker(A)

 (8) <2,4,-2,4,-2> is in ker(A)

 

 

 

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