Solved: Consider the problem of determining whether the

Chapter , Problem 7E

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QUESTION:

Consider the problem of determining whether the following system of equations is consistent for all \(b_1, b_2, b_3\):

\(\begin{aligned} 2 x_{1}-4 x_{2}-2 x_{3} &=b_{1} \\ -5 x_{1}+x_{2}+x_{3} &=b_{2} \\ 7 x_{1}-5 x_{2}-3 x_{3} &=b_{3} \end{aligned}\)

a. Define appropriate vectors, and restate the problem in terms of Span {\(v_1, v_2, v_3\)}. Then solve that problem.

b. Define an appropriate matrix, and restate the problem using the phrase “columns of A.”

c. Define an appropriate linear transformation T using the matrix in (b), and restate the problem in terms of T.

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QUESTION:

Consider the problem of determining whether the following system of equations is consistent for all \(b_1, b_2, b_3\):

\(\begin{aligned} 2 x_{1}-4 x_{2}-2 x_{3} &=b_{1} \\ -5 x_{1}+x_{2}+x_{3} &=b_{2} \\ 7 x_{1}-5 x_{2}-3 x_{3} &=b_{3} \end{aligned}\)

a. Define appropriate vectors, and restate the problem in terms of Span {\(v_1, v_2, v_3\)}. Then solve that problem.

b. Define an appropriate matrix, and restate the problem using the phrase “columns of A.”

c. Define an appropriate linear transformation T using the matrix in (b), and restate the problem in terms of T.

ANSWER:

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Consider the problem of determining whether the following system of equations is consistent for all b1, b2, b3

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