AB + AC = A(B + C)
True because this is the distributive property for matrices A, B, and C also mentioned in Theorem 2B.
The statement AB + AC = A(B + C) is true for any matrices A, B, and C of compatible sizes.
To see why this is true, we can use the distributive property of matrix multiplication over addition, which states that for any matrices A, B, and C of compatible sizes:
A(B + C) = AB + AC
Using this property, we can rewrite the left-hand side of the equation in the statement as follows:
AB + AC = A(B + C)
Therefore, the statement is true for any matrices A, B, and C of compatible sizes. Note that the distributive property of matrix multiplication over addition is similar to the distributive property of multiplication over addition in arithmetic.
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