In: Math
Determine whether S is a basis for R3.
S = {(4, 2, 5), (0, 2, 5), (0, 0, 5)}
S is a basis for R3.S is not a basis for R3.
If S is a basis for R3, then write
u = (8, 2, 15) as a linear combination of the
vectors in S. (Use s1,
s2, and s3, respectively,
as the vectors in S. If not possible, enter
IMPOSSIBLE.)
u =
Solution: Given:
To show:
is a basis of
Let
Consider
Any
vector in
can be written as a linear combination of vectors in
To check:
is linearly independent
Consider
is
linearly independent
is a basis of
To show:
is a linear combination of vectors in
Put
in