Solve the Problem $A = \left[ \begin{array} { r r r } 2 & - 5 & 3 \\ - 2 & 6 & - 5 \\ - 4 & 7 & 0 \end{array} \right]$

question 49

Multiple Choice

Solve the problem.
-Describe all solutions of Ax = b, where $A = \left[ \begin{array} { r r r } 2 & - 5 & 3 \\ - 2 & 6 & - 5 \\ - 4 & 7 & 0 \end{array} \right]$ and $\mathbf { b } = \left[ \begin{array} { r } - 3 \\ 4 \\ 3 \end{array} \right]$
Describe the general solution in parametric vector form.

• A) \(\left[ \begin{array} { l } x _ { 1 } \\ x _ { 2 } \\ x _ { 3 } \end{array} \right] = \left[ \begin{array} { r } 7 / 2 \\ 2 \\ 1 \end{array} \right] + x _ { 3 } \left[ \begin{array} { l } 1 \\ 1 \\ 0 \end{array} \right]\)
• B)
• \[\left[ \begin{array} { l }
• x _ { 1 } \\
• x _ { 2 } \\
• x _ { 3 }
• \end{array} \right] = \left[ \begin{array} { l }
• 1 \\
• 1 \\
• 0
• \end{array} \right] + x _ { 3 } \left[ \begin{array} { r }
• 7 / 2 \\
• 2 \\
• 0
• \end{array} \right]\]
• C)
• \[\left[ \begin{array} { l }
• x _ { 1 } \\
• x _ { 2 } \\
• x _ { 3 }
• \end{array} \right] = \left[ \begin{array} { l }
• 1 \\
• 1 \\
• 0
• \end{array} \right] + x _ { 3 } \left[ \begin{array} { r }
• 7 / 2 \\
• 2 \\
• 1
• \end{array} \right]\]
• D)
• \[\left[ \begin{array} { l }
• x _ { 1 } \\
• x _ { 2 } \\
• x _ { 3 }
• \end{array} \right] = \left[ \begin{array} { r }
• - 3 \\
• 1 \\
• 0
• \end{array} \right] + x _ { 3 } \left[ \begin{array} { r }
• - 1 \\
• 2 \\
• 1
• \end{array} \right]\]

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