# Vectors

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The set of vectors {[ 1 -1] , [ 1 -1] , [ 2 -1] }

[ 2 0 ] [ -1 0] [ -1 0]

from M_2(R) is:

A. linearly dependent

B. linearly independent

C. orthogonal

D. a spanning set for M_2(R)

E. a basis for M_2(R)

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##### Solution Summary

This shows how to determine the type of vectors from a matrix.

##### Solution Preview

I presume that each vector in this set is a 2*2 matrix. Then we have:

{[ 1 -1] , [ 1 -1] , [ 2 -1] }

[ 2 0 ] [ -1 0] [ -1 0]

part a and b.

Consider

[1 -1]

A1 :=

[2 0]

[1 -1]

A2 :=

[-1 0]

[2 -1]

A3 :=

[-1 0]

Then we define mA1+nA2+pA3=0 (zero matrix) and solve for m, n and p:

...

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