I believe it should be (c)?
Answer:
C₂₃ = -186
↓
C₁₃ = -32
↓
C₃₁ = 6
↓
C₁₁ = 27
↓
C₂₁ = 28
↓
C₃₃ = 38
↓
C₂₂ = 56
↓
C₃₂ = 90
↓
C₁₂ = 115
Step-by-step explanation:
The given matrices are;
![B = \left[\begin{array}{ccc}5&1&7\\3&15&-2\\-1&-9&25\end{array}\right]](https://tex.z-dn.net/?f=B%20%3D%20%5Cleft%5B%5Cbegin%7Barray%7D%7Bccc%7D5%261%267%5C%5C3%2615%26-2%5C%5C-1%26-9%2625%5Cend%7Barray%7D%5Cright%5D)
The cross product of the matrices is found as follows;
![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]](https://tex.z-dn.net/?f=A%20%5Ccdot%20B%20%3D%20%20%5Cleft%5B%5Cbegin%7Barray%7D%7Bccc%7D1%267%26-1%5C%5C5%26-2%26-9%5C%5C-3%268%263%5Cend%7Barray%7D%5Cright%5D%20%5Ctimes%20%5Cleft%5B%5Cbegin%7Barray%7D%7Bccc%7D5%261%267%5C%5C3%2615%26-2%5C%5C-1%26-9%2625%5Cend%7Barray%7D%5Cright%5D)
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;
![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]](https://tex.z-dn.net/?f=A%20%5Ccdot%20B%20%3D%20%20%5Cleft%5B%5Cbegin%7Barray%7D%7Bccc%7D1%267%26-1%5C%5C5%26-2%26-9%5C%5C-3%268%263%5Cend%7Barray%7D%5Cright%5D%20%5Ctimes%20%5Cleft%5B%5Cbegin%7Barray%7D%7Bccc%7D5%261%267%5C%5C3%2615%26-2%5C%5C-1%26-9%2625%5Cend%7Barray%7D%5Cright%5D%20%3D%20%5Cleft%5B%5Cbegin%7Barray%7D%7Bccc%7D27%26115%26-32%5C%5C28%2656%26-186%5C%5C6%2690%2638%5Cend%7Barray%7D%5Cright%5D)
In increasing order, we have;
C₂₃ = -186
↓
C₁₃ = -32
↓
C₃₁ = 6
↓
C₁₁ = 27
↓
C₂₁ = 28
↓
C₃₃ = 38
↓
C₂₂ = 56
↓
C₃₂ = 90
↓
C₁₂ = 115
The recipe calls for 3.25 cups of flour and we want to use 0.25 of that. We can multiply the two numbers together to get 0.25 of 3.25 cups.
3.25 * 0.25 = 0.8125 cups