Find the Matrix Product When Possible $A = \left[ \begin{array} { r r r } 0 & - 1 & 0 \\ 0 & 1 & 1 \\ - 1 & 0 & - 1 \end{array} \right]$

question 134

Multiple Choice

Find the matrix product when possible.
-Given $A = \left[ \begin{array} { r r r } 0 & - 1 & 0 \\ 0 & 1 & 1 \\ - 1 & 0 & - 1 \end{array} \right]$ and $B = \left[ \begin{array} { r r r } - 1 & 1 & 0 \\ 0 & - 1 & 0 \\ 1 & 1 & 0 \end{array} \right]$ , find $A B$ and $B A$ .

• A)
• \(\mathrm { AB } = \left[ \begin{array} { r r r } 0 & - 1 & 0 \\ 0 & - 1 & 0 \\ - 1 & 0 & 0 \end{array} \right] ; \mathrm { BA } = \left[ \begin{array} { r r r } 0 & - 1 & 0 \\ 0 & - 1 & 0 \\ - 1 & 0 & 0 \end{array} \right]\)
• B)
• \(\mathrm { AB } = \left[ \begin{array} { c c c } 0 & 2 & 1 \\ 0 & - 1 & - 1 \\ 0 & 0 & 1 \end{array} \right] ; \mathrm { BA } = \left[ \begin{array} { c c c } 0 & 1 & 0 \\ 1 & 0 & 0 \\ 0 & - 2 & 0 \end{array} \right]\)
• C)
• \(A B = \left[ \begin{array} { r r r } 0 & - 1 & 0 \\ 1 & 2 & 0 \\ 0 & - 2 & 0 \end{array} \right] ; B A = \left[ \begin{array} { c c c } 0 & 0 & - 1 \\ 0 & 1 & 1 \\ 0 & - 2 & - 1 \end{array} \right]\)
• D)
• \(\mathrm { AB } = \left[ \begin{array} { r r r } 0 & 1 & 0 \\ 1 & 0 & 0 \\ 0 & - 2 & 0 \end{array} \right] ; \mathrm { BA } = \left[ \begin{array} { c c c } 0 & 2 & 1 \\ 0 & - 1 & - 1 \\ 0 & 0 & 1 \end{array} \right]\)

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Definitions:

Frequency

The rate at which a cyclic or periodic event occurs, typically measured in cycles per unit time.

Timbre

The characteristic of a sound that makes it identifiable from other sounds with the same pitch and loudness.

Purity

The state or quality of being clean, free from contaminants, or morally untarnished.

Variation in Contrast

Differences in the degree of distinction between two or more elements, often used in visual and language analysis.