**Question:**There are 6 linearly independent vectors in \(\mathbb{R}^5\).- ○ True- ○ False**Explanation:**In the vector space \(\mathbb{R}^5\), a maximum of 5 linearly independent vectors can exist because the dimension of \(\mathbb{R}^5\) is 5. Therefore, the statement that there are 6 linearly independent vectors in \(\mathbb{R}^5\) is false.

We know that the dimension of the vector space R5 is 5.

Answered: There are 6 linearly independent…

Math

Algebra

There are 6 linearly independent vectors in R°. O True False

Algebra and Trigonometry (6th Edition)

6th Edition

ISBN:9780134463216

Author:Robert F. Blitzer

Publisher:Robert F. Blitzer

ChapterP: Prerequisites: Fundamental Concepts Of Algebra

Section: Chapter Questions

Problem 1MCCP: In Exercises 1-25, simplify the given expression or perform the indicated operation (and simplify,...

See similar textbooks

Similar questions

Find two vectors in opposite directions that are orthogonal to the vector u. (The answers are not unique. Enter your answer as a comma-separated list of vectors.) = (6, -5, 8)
Let v = (1,0, -2), v2 = (-2, 1,7), v3 = (h,-3,–5) be three vectors in R. For what value(s) of h is v, spanned by v, and y,? Answer: h = -3 h+-2 Ch#2 ch = 2 The co FINISH REVIEW
Show whether the vector w is a linear combination of vectors v1, v2 and v3 where w = 2 v2 v3 [2]
U1 = U₂ = Evaluate the following linear combination of two vectors. ²9+³8-D +3 = U1 U2
Determine if b is a linear combination of the other vectors. If so, express b as a linear combination. (If b cannot be written as a linear combination of the other two vectors, enter DNE in both answer blanks.) a = a, = b = Jas + ( 2 b =
Which pairs of vectors are parallel? Select all that apply. OA. 10i – 15k, –4i + 6k В. 3і + 4j, —12i — 12j — 4k OC. 6і + 5k, 6і + 12) OD. -2i + 4j + 5k, 4i – 8j – 10k E. Зі — 2j + 5k, —6і + 6ј — 15k
Express the indicated vector w as a linear combination of the given vectors v1 and v2 if this is possible. If not, show that it is impossible. w= (-1,0,7), V1= (7,6,5), v2=(6,5,3) Select the correct answer below, and fill in the answerbox(es) to complete your choice. A.It is possible to express the vector w in terms of v1 and v2, as w=(___)v1+(___)v2. (Type integers or fractions.) B.It is impossible to express the vector w in terms of v1 and v2, because an echelon form of the augmented matrix [v1 v2 w], E=___?, shows that the system is inconsistent.