Mathematics, 17.10.2020 01:01 kimseokjin92
LINEAR ALGEBRA Suppose u1= [2,3,1] and u2= [4,1,0]. For which value(s) of the constant k is [1,2,k] a linear combination of u1 and u2?
Answers: 1
so that 
is a linear combination of 
and 
is 
.![\vec u_{1} = [2,3,1]](/tpl/images/0814/8408/89ab7.png)
, ![\vec u_{2} = [4,1,0]](/tpl/images/0814/8408/77683.png)
and ![\vec u_{3} = [1, 2,k]](/tpl/images/0814/8408/387bc.png)
, 
(Eq. 1)
, 
, 
- Scalar coefficients of linear combination, dimensionless.
(Eq. 2)
- Zero vector, dimensionless.![[1,2,k] = -\lambda_{1}\cdot [2,3,1]-\lambda_{2}\cdot [4,1,0]](/tpl/images/0814/8408/18f4b.png)
![[1,2,k] = [-2\cdot\lambda_{1},-3\cdot \lambda_{1},-\lambda_{1}]+[-4\cdot \lambda_{2},-\lambda_{2},0]](/tpl/images/0814/8408/a46a4.png)
![[0,0,0] = [-2\cdot \lambda_{1},-3\cdot \lambda_{1},-\lambda_{1}]+[-4\cdot \lambda_{2},-\lambda_{2},0]+[-1,-2,-k]](/tpl/images/0814/8408/f5807.png)
![[-2\cdot \lambda_{1}-4\cdot \lambda_{2}-1,-3\cdot \lambda_{1}-\lambda_{2}-2,-\lambda_{1}-k] =[0,0,0]](/tpl/images/0814/8408/0288f.png)
(Eq. 3)
(Eq. 4)
(Eq. 5)
, 
, 
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LINEAR ALGEBRA
Suppose u1= [2,3,1] and u2= [4,1,0]. For which value(s) of the constant k is [1,2,k]...
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