Solve the System of Linear Equations Using the Inverse Matrix

question 80

Multiple Choice

Solve the system of linear equations $\left\{ \begin{array} { l l } 5 x _ { 1 } - 10 x _ { 2 } - 5 x _ { 3 } - 10 x _ { 4 } & = 0 \\15 x _ { 1 } - 25 x _ { 2 } - 10 x _ { 3 } - 15 x _ { 4 } & = 8 \\10 x _ { 1 } - 25 x _ { 2 } - 10 x _ { 3 } - 25 x _ { 4 } & = - 8 \\- 5 x _ { 1 } + 20 x _ { 2 } + 20 x _ { 3 } + 55 x _ { 4 } & = 16\end{array} \right.$ using the inverse matrix $\frac { 1 } { 5 } \left[ \begin{array} { c c c c } - 24 & 7 & 1 & - 2 \\- 10 & 3 & 0 & - 1 \\- 29 & 7 & 3 & - 2 \\12 & - 3 & - 1 & 1\end{array} \right]$ .

• A) \(\left[ \begin{array} { l }
• x _ { 1 } \\
• x _ { 2 } \\
• x _ { 3 } \\
• x _ { 4 }
• \end{array} \right] = \left[ \begin{array} { c }
• \frac { 16 } { 5 } \\
• \frac { 8 } { 5 } \\
• \frac { - 8 } { 5 } \\
• \frac { - 16 } { 5 }
• \end{array} \right]\)
• B) \(\left[ \begin{array} { l }
• x _ { 1 } \\
• x _ { 2 } \\
• x _ { 3 } \\
• x _ { 4 }
• \end{array} \right] = \left[ \begin{array} { c }
• 0 \\
• \frac { 8 } { 5 } \\
• 0 \\
• \frac { 16 } { 5 }
• \end{array} \right]\)
• C) \(\left[ \begin{array} { l }
• x _ { 1 } \\
• x _ { 2 } \\
• x _ { 3 } \\
• x _ { 4 }
• \end{array} \right] = \left[ \begin{array} { c }
• \frac { 16 } { 5 } \\
• \frac { 8 } { 5 } \\
• 0 \\
• 0
• \end{array} \right]\)
• D) \(\left[ \begin{array} { l }
• x _ { 1 } \\
• x _ { 2 } \\
• x _ { 3 } \\
• x _ { 4 }
• \end{array} \right] = \left[ \begin{array} { c }
• \frac { 24 } { 5 } \\
• \frac { - 8 } { 5 } \\
• 0 \\
• \frac { - 16 } { 5 }
• \end{array} \right]\)
• E) \(\left[ \begin{array} { l }
• x _ { 1 } \\
• x _ { 2 } \\
• x _ { 3 } \\
• x _ { 4 }
• \end{array} \right] = \left[ \begin{array} { c }
• \frac { 24 } { 5 } \\
• \frac { - 8 } { 5 } \\
• \frac { - 16 } { 5 } \\
• \frac { 16 } { 5 }
• \end{array} \right]\)

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Definitions:

Lunar Highlands

Rough, mountainous regions on the moon's surface, characterized by their lighter color and higher altitude than the lunar maria.

Mare

Latin for "sea," often used to describe the large, dark basaltic plains on the Moon, formed by ancient volcanic eruptions.

Lunar Highlands

Elevated, mountainous regions on the moon's surface, characterized by high albedo, heavy cratering, and made predominantly of anorthosite.

Impact Craters

Circular depressions formed by the collision of a meteorite, asteroid, or comet with the Earth's surface, characterized by a raised rim and, in some cases, a central peak.