Advanced Search

Question: Rank in vectors

Question:Rank in vectors

rameen hamood 30 Maple
linear-algebra homework rank subspace do-my-homework-for-me
July 28 2020
1

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

 

im(A)={y:y=Ax for some x∈Rn} ,

 

which is a vector space.

The dimension of im(A)  is called the rank of A, denoted by rank(A) .

(a)  Find the rank of the matrix 

v1:=<-146, -84, 28, -154>

v2:=<-203, 106, 34, -181>

v3:=<-94, -4, 106, -154>

v4:=<-36, 152, -86, 50>

v5:=< 173, 122, -390, 435>

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

and enter in the box below.

rank(A)=    

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

(1) <97,-8,-49,-66> is in im(A)

(2) <-65,74,10,-52> is in im(A)

(3)im(A) is subspace of R^4

(4) <2,-2,-4,4,-2> is in im(A)

(5) <0,0,0,0> is in im(A)

(6) <0,0,0,0,0> is in im(A)

(7) <-1,-2,1,-2,1> is in im(A)

(8) im(A) is a subspace of R^5
Please Wait...