Answer to Question #46812 in Vector Calculus for irebami

Question #46812

If
r4=r1+r2+r3
,which of the vectors are linearly dependent .

r1
r3
r4
r2

Expert's answer

All four vectors r1, r2, r3, r4 are linearly dependent. To answer whether r1, r2, r3 are linearly dependent, we need more information on these vectors.

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Assignment Expert

07.09.15, 20:45

Vectors r1, r2, r3 may constitute either a linearly independent set (for example, (1,0,0), (0,1,0),(0,01) ) or a linearly dependent set (for example, r1=r2=(1,0,0), r3=2r1=2r3=(2,0,0)). Thus, r1, r2, r3 do not always constitute a linearly independent set, though they may.

chimex4ever1

07.09.15, 16:13

If you can represent the sum of given vectors r1, r2 and r3 by a single vector r4 i. e. r4 = r1 + r2 + r3. Then you can say r4 is linearly dependent on r1, r2 and r3 and that r1, r2, r3 and r4 constitute a linearly dependent set of vectors. On the other hand r1, r2 and r3 are linearly independent vectors ANSWER IS r4

Answer to Question #46812 in Vector Calculus for irebami

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