Question
Match the following with the picture.
1. False it could be that v4 is the zero vector
2. True rank(A) <# of columns of A
3. False since there is a dependence relation for the vectors
4.7
5. False since rank(A) <=4<5=# COLUMNS OF A
6.True since([v1v2v3v4])=4 and therefore rank([v1v2v3])=4
7.False since rank(A)<=5<6
8.5
9.True since rank[v1v2v3] is less than 3 and therefore rank([v1v2v3v4]) is less than 4
10.at least 8
11. at leat 7
12.8
13.false since it could that v1=0 and v2=0
14. True since rank(A) =# of columns of A
15.4
TRUE or FALSE? If vi, V2 are vectors in Rs such that v2 is not a scalar multiple of v then vi and v2 are linearly independent. Choose TRUE or FALSE? If v1,V2,vs and v4 are linear independent vectors in Rn, then vi,V2,vs are also linear independent. Choose What is the rank of a 7x5 matrix A if its column vectors are linearly independent? Choose TRUE or FALSE? If the columns of the matrix A are linearly independent, then the homogeneous system AX-0 has only the trivial solution Choose TRUE Oor FALSE? If the REF of a 5x5 matrix has a zero row, then the columns of A are linearlyChoose independent. TRUE or FALSE? If A is a 5x6 matrix, then its column vectors are linearly independent? Choose How many row must a matrix have if its columns are linearly independent and it has 7 columns? Choose TRUE or FALSE? If Vi, V2, Vs are vectors such that 2v1 - 3v2 + 5Vs 0, then vi, V2, Choose vs are linearly independent. TRUE or FALSE? Choose If a matrix A has a zero column, then its columns are linearly dependent. TRUE or FALSE? If the homogeneous system Ax 0, has a non-zero solution, then the Choose column vectors of A are linearly dependent What is the rank of a 4x4 matrix with linearly independent columns? Choose TRUE or FALSE? If V1,V2,V3 and v4 are vectors such that vi,V2,V3 are linear independent, then vi,Vz,Vs and va are also linear independent Choose TRUE or FALSE? If V1,V2,Vs and V4 are vectors in Rn such that v1,V2,Vs are linear dependent, then v1,V2,Vs and va are also linear dependent. Choose
Explanation / Answer
1. True.
2. True.
3. The rank of A is 5 as the column and row ranks of a matrix are equal.
4. True.
5. False. The columns can be linearly dependent also.
6. False. The maximum rank of A is 5 so that its 6 columns have to be linearly dependent.
7. The matrix must have atleast 7 rows .
Please post the remaining questions again, maximum 4 at a time.
