The expression of v = (2,1,5) as a linear combination of (1,2,1), (1,0,2) and (1,1,0) is [tex](2,1,5)=1(1,2,1)+2(1,0,2)+-1(1,1,0)[/tex]
To express v= (2,1,5) as a linear combination of (1,2,1), (1,0,2) and (1,1,0), it will be written as:
[tex](2,1,5)=x(1,2,1)+y(1,0,2)+z(1,1,0)[/tex]
This will yield the following equations:
x + y + z = 2........(1)
2x + z = 1..........(2)
x + 2y = 5........(3)
The solution to the system of equations above is:
x = 1, y = 2, z = -1
Therefore, the linear combination is:
[tex](2,1,5)=1(1,2,1)+2(1,0,2)+-1(1,1,0)[/tex]
Learn more on linear combinations here:https://brainly.com/question/17407318
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