please show your work (1 pt) Which of the following sets of vectors are linearly independent? A....

Question:

please show your work (1 pt) Which of the following sets of vectors are linearly independent?

A. {(-1,8), (9, -1) }

B. {(6, -3)}

C. {(4, -7, 1, 7), 1, -5, 2, -9)}

D.{ (-2, -5, -8), (-9, 2, 4), (-7, 12, 7), (-2, 11 --7)}

E. {(0, 0)}

F. {(-7, 2, 00), -8, -5, -6), 1, -4, 9)}

G. {(-2, -4), (0, 0) }

H. {(-8, -9), 2, 4), (5, 7)}

Linearly Independent Vectors:

A set consisting of single non-zero vector is linearly independent.

Aset consisting of two vectors is said to be linarly independent if they are not multiples of each other.

On forming a matrix in the form of determinant, if value of determinant is non-zero then set of vectors is said to be linearly independent.

If a set contains more vectors than there are entries in each vector, then the set is linearly dependent.

A set containing zero vector is linearly dependent.

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A.

{eq}\left \{ \left ( -1,8 \right ),\left ( 9,-1 \right ) \right \} {/eq}

Linearly independent as they are not multiples of each other.

B.

{eq}...

Vectors: Definition, Types & Examples

from

Chapter 57 / Lesson 3
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