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s v1, v2, v3, and b in 2, shown in the figure. Does the
Chapter 1, Problem 32E(choose chapter or problem)
PROBLEM 32EConsider the vectors v1, v2, v3, and b in ?2, shown in the figure. Does the equation x1v1 + x2v2 + x3v3 = b have a solution? Is the solution unique? Use the figure to explain your answers.
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QUESTION:
PROBLEM 32EConsider the vectors v1, v2, v3, and b in ?2, shown in the figure. Does the equation x1v1 + x2v2 + x3v3 = b have a solution? Is the solution unique? Use the figure to explain your answers.
ANSWER:SolutionStep 1 of 2Consider the vectors v1, v2, v3, and b in 2 and the vector b is a linear combination of v1 ,v2 and v3b = x1v1 + x2v2 + x3v3Since v1 and v2 are the scalar multiple , so the Span {v1,v2} are in all R2. Therefore the vector b is a linear combination of v1 and v2 b = x1v1 + x2v2So, according to the figure vector b is not a scalar multiple of v1 vector.So, x2 0. Therefore the equation has a solution.