Question

Arrange the entries of matrix AB in increasing order of their values. Okay

Answer 1

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;

$A = \left[\begin{array}{ccc}1&7&-1\\5&-2&-9\\-3&8&3\end{array}\right]$      $B = \left[\begin{array}{ccc}5&1&7\\3&15&-2\\-1&-9&25\end{array}\right]$

The cross product of the matrices is found as follows;

$A \cdot B = \left[\begin{array}{ccc}1&7&-1\\5&-2&-9\\-3&8&3\end{array}\right] \times \left[\begin{array}{ccc}5&1&7\\3&15&-2\\-1&-9&25\end{array}\right]$

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;

$A \cdot B = \left[\begin{array}{ccc}1&7&-1\\5&-2&-9\\-3&8&3\end{array}\right] \times \left[\begin{array}{ccc}5&1&7\\3&15&-2\\-1&-9&25\end{array}\right] = \left[\begin{array}{ccc}27&115&-32\\28&56&-186\\6&90&38\end{array}\right]$

In increasing order, we have;

C₂₃ = -186

      ${}$    ↓

C₁₃ = -32

      ${}$    ↓

C₃₁ = 6

      ${}$    ↓

C₁₁ = 27

      ${}$    ↓

C₂₁ = 28

      ${}$    ↓

C₃₃ = 38

      ${}$    ↓

C₂₂ = 56

      ${}$    ↓

C₃₂ = 90

      ${}$    ↓

C₁₂ = 115