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Express the vector as a linear combination of vectors A and B?

User Sladomic
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Final Answer:

To express the vector as a linear combination of vectors A and B we represent them as V = 2A - 3B

Step-by-step explanation:

To express the vector
\(\mathbf{V}\) as a linear combination of vectors
\(\mathbf{A}\)and
\(\mathbf{B}\), we find scalar multiples of
\(\mathbf{A}\) and
\(\mathbf{B}\) such that their sum equals
\(\mathbf{V}\). Let x and y be the scalars, then
\(\mathbf{V} = x\mathbf{A} + y\mathbf{B}\). By comparing components, we get two equations: 2x - 3y = 1 and 5x + 2y = -5. Solving this system yields x = 2 and y = -3, leading to the linear combination
\(\mathbf{V} = 2\mathbf{A} - 3\mathbf{B}\).

Linear combinations involve expressing a vector as a sum of scalar multiples of other vectors. The coefficients in this combination represent the weights of each vector. Solving a system of linear equations allows finding these coefficients, providing a concise representation of the original vector in terms of the given vectors.

User Jamie De Palmenaer
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