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If i have 3 4x1 matrices and i want to check if i can express a 4th matrix as the linear combination of the first 3.

my 3 vectors:

1 7 -2

4 10 1

2 -4 5

-3 -1 -4

can this vector be expressed a linear combination of the first 3:

54

0

-108

78

my attempt:

i made a big matrix out of them:

1 7 -2 c1 54

4 10 1 c2 0

2 -4 5 c3 -108

-3 -1 -4 c4 78

i do gaussian elimination:

1 0 1.5 -30

0 1 -.5 12

or

c1 + 1.5c2 = -30

c2 - .5c3

not sure what to do now.

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# Homework Help: Linear combinations?

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