Find A(B + C) - 14I.

Given:

A = [[1,3],[2,4]]

B = [[1,2],[2,4]]

C = [[4,1],[1,5]]

I = [[1,0],[0,1]]

Required: A(B + C) − 14I

First:

B + C

= [[1+4, 2+1], [2+1, 4+5]]

= [[5,3], [3,9]]

Now:

A(B+C)

= [[1,3],[2,4]] [[5,3],[3,9]]

= [[1×5 + 3×3, 1×3 + 3×9], [2×5 + 4×3, 2×3 + 4×9]]

= [[14,30], [22,42]]

Also:

14I

= [[14,0], [0,14]]

Therefore:

A(B+C) − 14I

= [[14,30],[22,42]] − [[14,0],[0,14]]

= [[0,30], [22,28]]

Answer:

[[0,30],[22,28]].

Matrix addition is performed first, followed by row-by-column multiplication and finally subtraction of 14I.