Answer:
The value of the constant so that
is a linear combination of
and
is
.
Step-by-step explanation:
Let be ,
and
,
is a linear combination of
and
if and only if:
(Eq. 1)
Where:
,
,
- Scalar coefficients of linear combination, dimensionless.
By dividing each term by :
(Eq. 2)
- Zero vector, dimensionless.
And all vectors are linearly independent, meaning that at least one coefficient must be different from zero. Now we expand (Eq. 2) by direct substitution and simplify the resulting expression:
The following system of linear equations is obtained:
(Eq. 3)
(Eq. 4)
(Eq. 5)
The solution of this system is:
,
,
The value of the constant so that
is a linear combination of
and
is
.
