In
R^(3)
we consider the following vectors
vec(v)_(1)=(1,2,3),vec(v)_(2)(1,1,-1),vec(v)_(3)=(2,1,-4),vec(v)_(4)=(2,2,2)
a) Is
(vec(v)_(1),vec(v)_(2))
a basis of
R^(3)
? (no calculation needed). Justify the answer b) Is
(vec(v_(1)),vec(v_(2)),vec(v_(3)),vec(v_(4)))_(a )
basis of
R^(3)
? (no calculation needed). Justify the answer c) Let
B
be the family
(vec(v)_(1),vec(v)_(2),vec(v)_(3))
. Write
M_(B)
its canonical matrix and calculate the determinant of
M_(B)
. Justify that
B
is a basis of
R^(3)
. d) Calculate the imvere of
M_(B)
by the method of your choice. e) What are the coordinater of
vec(v)_(uarr)
in the basis
B
.