Question
In: Math
Determine which of the following sets of vectors form a basis for R 3 . S...
Determine which of the following sets of vectors form a basis for R 3 . S = {(1, 0, −1),(2, 5, 1),(0, −4, 3)}, T = {(−1, 3, 2),(3, −1, −3),(1, 5, 1)}.
Solutions
Expert Solution
Solution:
Check whether 
is linearly independent.
Let 
This in matrix form is
By 
By 
is linearly independent.
Check 
.
Let 
.
To find 
such that 
.
This in matrix form is
By
By
.
.
Hence, 
is the basis of 
.
--------------------------------------------------------------------------------------------------------------------------------
Check whether 
is linearly independent.
Let 
This in matrix form is
By 
By 
Since the rank of the matrix is less than the number of unknown
, there is 
free variable.
Since
are not zero , 
is linearly dependent and hence not a basis of
.
milcah answered 2 years agoRelated Solutions
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