(a) Explanation Formula used: Addition in M m × n ( ℝ ) is defined by [ a i j ] m × n + [ b i j ] m × n = [ c i j ] m × n , where c i j = a i j + b i j . Proof: Let A = [ a i j ] m × n is any element in M m × n ( ℝ ) . O m × n denote the m × n matrices that has all elements zero. Let − A = [ − a i j ] m × n is element of M m × n ( ℝ ) (b) To determine To prove: Addition is commutative in M m × n ( ℝ ) .

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Author: Gilbert, Linda, Jimmie

Publisher: Cengage Learning,

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Chapter 1.6, Problem 16E

(a)

To determine

To prove: Addition in Mm × n(ℝ) has the property that each element in Mm × n(ℝ) has an additive inverse in Mm × n(ℝ).

(b)

To determine

To prove: Addition is commutative in Mm × n(ℝ).

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Chapter 1.6, Problem 15E

Chapter 1.6, Problem 17E

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To prove: Addition in M m × n ( ℝ ) has the property that each element in M m × n ( ℝ ) has an additive inverse in M m × n ( ℝ ) .

Solution Summary: The author explains the formula used to prove that addition in M_mtimes has an additive inverse.

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To prove: Addition in Mm × n(ℝ) has the property that each element in Mm × n(ℝ) has an additive inverse in Mm × n(ℝ).

To prove: Addition is commutative in Mm × n(ℝ).

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