002] is the correct definition of Linear Independence correct def he following 1

Question

002] is the correct definition of Linear Independence correct def he following 14. Which of the following (a) A list of vectors v1,02, ..,jk in a vector space is said to be linea earl p,., k in a vector space is said to b aj independent if quit c2U2 + + ckUk = 0 when all theco C1, C2, ,Ch are zero. (b) A list of vectors u1,V2, , ve in a vector space is said to be independent if cv2+0 implies that c1 +02+ inearly (e) A list of vectors v1, U2,.., e in a vector space is said to be linearly independent if the following statement is true:

Explanation / Answer

The statement a) is wrong because if all constant are zero then its obvious that linear combination is also zero.

B) is also wrong. Counter example is v1=v2=(1 0). c1=1,c2=-1 .

This satisfy equation but v1 and v2 is not imdependent.

C) is true..

D) is almost same as A). So false

E) is also not true

Related Questions

Navigate

• Browse (All)
• Browse
• Subjects

---

---

Integrity-first tutoring: explanations and feedback only — we do not complete graded work. Learn more.