Compute the Determinant of the Matrix $2 \times 2$ Matrix to Calculate the Inverse of the Given Matrix

question 16

Multiple Choice

Compute the determinant of the matrix. If the determinant is nonzero, use the formula for inverting a $2 \times 2$ matrix to calculate the inverse of the given matrix. $\left[ \begin{array} { c c } 1 & 2 \\2 & - 1\end{array} \right]$

• A)-5; \(\left[ \begin{array} { c c }
• \frac { 1 } { 5 } & \frac { 2 } { 5 } \\
• \frac { 2 } { 5 } & - \frac { 1 } { 5 }
• \end{array} \right]\)
• B) -10; \(\left[ \begin{array} { l l }
• \frac { 1 } { 5 } & \frac { 2 } { 5 } \\
• \frac { 2 } { 5 } & \frac { 1 } { 5 }
• \end{array} \right]\)
• C) 5; \(\left[ \begin{array} { l }
• - \frac { 1 } { 5 } - \frac { 2 } { 5 } \\
• - \frac { 2 } { 5 } \quad \frac { 1 } { 5 }
• \end{array} \right.\)
• D) -4; \(\left[ \begin{array} { l }
• - \frac { 1 } { 5 } - \frac { 2 } { 5 } \\
• - \frac { 2 } { 5 } \quad \frac { 1 } { 5 }
• \end{array} \right.\)
• E) -10; \(\left[ \begin{array} { c c }
• \frac { 1 } { 5 } & \frac { 2 } { 5 } \\
• \frac { 2 } { 5 } & - \frac { 1 } { 5 }
• \end{array} \right]\)

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Definitions:

Qualitative

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Deductive

A logical process wherein a conclusion is based on the concordance of multiple premises that are generally assumed to be true.

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A method of reasoning in which general principles are derived from specific observations.