Question

Express v= (2,1,5) as a linear combination of (1,2,1), (1,0,2) and (1,1,0)

Answer 1

The expression of v = (2,1,5) as a linear combination of (1,2,1), (1,0,2) and (1,1,0) is $(2,1,5)=1(1,2,1)+2(1,0,2)+-1(1,1,0)$

Linear Combinations

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:

$(2,1,5)=x(1,2,1)+y(1,0,2)+z(1,1,0)$

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:

$(2,1,5)=1(1,2,1)+2(1,0,2)+-1(1,1,0)$

Learn more on linear combinations here:brainly.com/question/17407318

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