1.li since rank([v1v2v3v4])=4=# of vectors 2.h=3 3.Id since rank(u?=0<1=#OF VECT
ID: 3185986 • Letter: 1
Question
1.li since rank([v1v2v3v4])=4=# of vectors
2.h=3
3.Id since rank(u?=0<1=#OF VECTORS
4.H CAN BE ANY REAL NUMBER
5.Id since max# of Li vectors in R^3 is 3
6.Li subce rank(A)=3=#of columns
7.Id since v2 is linear combination of v1 v3 v4
8.h=7
9.h can be any real number except -8
10. li since v2 is not linear combination of v1and v1 is not a lc of v2
11.Id since max# of li vectors in R^2 is 2
12.h=-2
13. Li since rank(u)=1=# of vectors
14.Id since v2 is a lc (multiple) of v1
match the picture with 1-14
Are the gien vectors ld or I? Aen vectors Choosc -3-15 Are the siven vectors d cr E Choose. Linear dopandent or linear independent? Choose Find values fh such that the flowing vectors are li. nd all values of h such that the cokuriri vecturs of A are hrieer dependent. 2 -5 8 -3 4 Are the given vectors dor li? Are the gien vechors d orE -4-3 0 0 -14 Choosc 1 0 3 Are the gien vectors ld or? 65 20 13 24 53 Lincar dependent ar lincar in ChooscExplanation / Answer
1. The dimension of R2 is 2. The given set has 4 vectors. Therefore, it is linearly dependent.
2. Since v2 = -5v1, hence the vectors v1,v2 are linearly dependent.
3. The inclusion of the zero vector makes the vectors v1,v2 linearly dependent.
4. u being a single vector, is linearly independent.
5. Let A = [v1,v2,v3] .
To answer the question, we will reduce A to its RREF as under:
i. Add -5 times row 1 multiplied by to row 2
ii. Add 3 times row 1 to row 3
iii. Add 2 times row 2 to row 1
iv. Add row 2 to row 3
v. Multiply row 2 by ?1
vi. Multiply row 3 by 1/ (h?6)
vii. Add 25 times row 3 to row 1
viii. Add -14 time row 3 to row 2
The RREF of A is I3.It may be observed that in the 6th row operation, we multiplied the 3rd row by 1/(h-6). This if possible only if h is not equal to 6. Thus, the given set of vectors is linearly independent if h is not equal to 6.
6. The RREF of A is
1
0
-(3h+28)/5
0
1
-(h+16)/5
0
0
0
The columns of A will be linearly dependent only if the 3rd column in the RREF is a linear combination of the 1st and the 2nd columns. If -(3h+28)/5 = 1 or, 3h+28 = -5 or, 3h = -33 or, h = -11. Then -(h+16)/5 = -(-11+16)/5 = -5/5 = -1. Thus, if h = -11, then c3= c1-c2 where c1,c2,c3 denote the 1st,2nd and 3rd columns of A. Hence the columns of A are linearly dependent if h = -11.
Please post the remaining questions again , maximum 4 at a time.
1
0
-(3h+28)/5
0
1
-(h+16)/5
0
0
0
Related Questions
Navigate
Integrity-first tutoring: explanations and feedback only — we do not complete graded work. Learn more.