Vectors
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)
https://brainmass.com/math/vector-calculus/type-vector-matrix-15916
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:
...
Solution Summary
This shows how to determine the type of vectors from a matrix.
$2.19