If A = [(1, 0, 1) (3, 1, 2)], B = [(2, 1, -4) (3, 5, -2)] and C = [(0, 2, 3) (-1, -1, 0)] , verify that (A + 2B + 3C)^T = A^T + 2B^T + 3C^T

Question

If A = \(\begin{vmatrix}1&0&1\\3&1&2\end{vmatrix}, B = \begin{vmatrix}2&1&-4\\3&5&-2\end{vmatrix} and\, C = \begin{vmatrix}0&2&3\\-1&-1&0\end{vmatrix}\), verify that (A + 2B + 3C)^T = A^T + 2B^T + 3C^T

A = [(1, 0, 1) (3, 1, 2)], B = [(2, 1, -4) (3, 5, -2)] and C = [(0, 2, 3) (-1, -1, 0)]

Answer 1

 A + 2B + 3C = \(\begin{vmatrix}1&0&1\\3&1&2\end{vmatrix}+ 2 \begin{vmatrix}2&1&-4\\3&5&-2\end{vmatrix} +3 \begin{vmatrix}0&2&3\\-1&-1&0\end{vmatrix}\)

∴ A + 2B + 3C = \(\begin{vmatrix}5&8&2\\6&8&-2\end{vmatrix}\)

From (i) and (ii), we get (A + 2B + 3C)^T = A^T + 2B^T + 3C^T