Question

for what value of k the vectors (1,-2,k) in R3 be a linear combination of vectors (3,0,-0) and (2,-1,5)?​

Answer 1

I HOPE IT HELPS YOU!!!!

Answer 2

Answer:

10

For linear combination of vectors the discriminant of the matrix of those three vectors should have the value 0.

3   0   0

2   -1   5     =     0

1    -2  k

[3((-1)(k)-(5)(-2)) - 0((2)(k)-(5)(1)) + 0((2)(-2)-(-1)(1))] = 0

3(-k+10)-0-0 = 0

3(10-k) = 0

10-k = 0

k = 10