Answer:
C₂₃ = -186
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C₁₃ = -32
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C₃₁ = 6
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C₁₁ = 27
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C₂₁ = 28
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C₃₃ = 38
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C₂₂ = 56
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C₃₂ = 90
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C₁₂ = 115
Step-by-step explanation:
The given matrices are;
[tex]A = \left[\begin{array}{ccc}1&7&-1\\5&-2&-9\\-3&8&3\end{array}\right][/tex] [tex]B = \left[\begin{array}{ccc}5&1&7\\3&15&-2\\-1&-9&25\end{array}\right][/tex]
The cross product of the matrices is found as follows;
[tex]A \cdot B = \left[\begin{array}{ccc}1&7&-1\\5&-2&-9\\-3&8&3\end{array}\right] \times \left[\begin{array}{ccc}5&1&7\\3&15&-2\\-1&-9&25\end{array}\right][/tex]
C₁₁ = 1×5 + 7×3 + (-1) × (-1) = 27
C₁₂ = 1×1 + 7×15 + (-1)×(-9) = 115
C₁₃ = 1×7 + 7×(-2) + (-1)×25 = -32
C₂₁ = 5×5 + (-2)×3 + (-9) × (-1) = 28
C₂₂ = 5×1 + (-2)×15 + (-9)×(-9) = 56
C₂₃ = 5×7 + (-2)×(-2) + (-9)×25 = -186
C₃₁ = (-3)×5 + 8×3 + 3 × (-1) = 6
C₃₂ = (-3)×1 + 8×15 + 3×(-9) = 90
C₃₃ = (-3)×7 + 8×(-2) + 3×25 = 38
Therefore, we get;
[tex]A \cdot B = \left[\begin{array}{ccc}1&7&-1\\5&-2&-9\\-3&8&3\end{array}\right] \times \left[\begin{array}{ccc}5&1&7\\3&15&-2\\-1&-9&25\end{array}\right] = \left[\begin{array}{ccc}27&115&-32\\28&56&-186\\6&90&38\end{array}\right][/tex]
In increasing order, we have;
C₂₃ = -186
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C₁₃ = -32
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C₃₁ = 6
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C₁₁ = 27
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C₂₁ = 28
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C₃₃ = 38
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C₂₂ = 56
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C₃₂ = 90
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C₁₂ = 115
