Find all scalars C, if any exist, such that given statement is true. i+ cj +(c-1)k i is in the span of i+2j + k and 3i +6j + 3k Thank you! Solution i+ cj +(c-1)k = a(i+2j + k) + b( 3i +6j + 3k) --> a + 3b = 1 (1) 2a + 6b = c (2) a + 3b = c - 1 (3) From (1) and (2): 2(a + 3b) = 2(1) --> 2a + 6b = 2 = c Therefore c = 2. You can also check that for c = 2, the third equation and the first equation are the same, So this values satisfies the third equation too..

1. Find all scalars C, if any exist, such that given statement is true.
i+ cj +(c-1)k i is in the span of i+2j + k and 3i +6j + 3k
Thank you!
Solution
i+ cj +(c-1)k = a(i+2j + k) + b( 3i +6j + 3k)
--> a + 3b = 1 (1)
2a + 6b = c (2)
a + 3b = c - 1 (3)
From (1) and (2):
2(a + 3b) = 2(1) --> 2a + 6b = 2 = c
Therefore c = 2.
You can also check that for c = 2, the third equation and the first equation are the same, So this
values satisfies the third equation too.