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# Solved: In this exercise we show that matrix ## Problem 12E Chapter 2.6

Discrete Mathematics and Its Applications | 7th Edition

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Problem 12E

In this exercise we show that matrix multiplication is distributive over matrix addition.a) Suppose that A and B arc m × k matrices and that C is a k × n matrix. Show that (A + B)C = AC + BC.________________b) Suppose that C is an m × k matrix and that A and B are k × n matrices. Show that C(A + B) = CA + CB.

Step-by-Step Solution:

SolutionStep 1:In this problem we have to show that matrix multiplication is distributive over matrix addition.Step 2: a) Suppose that A and B are m × k matrices and that C is a k × n matrix. Show that (A + B)C = AC + BC. Therefore (A+B) + Now (A+B)C (multiply C matrix with AXB) Which is Step 3: Take right hand side AC= Similarly BC= Adding both matric AC+BCWe get Therefore we can say (A + B)C = AC + BC Hence, it is proved that matrix multiplication is distributive over matrix addition.

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##### ISBN: 9780073383095

This textbook survival guide was created for the textbook: Discrete Mathematics and Its Applications, edition: 7th. This full solution covers the following key subjects: Matrix, show, suppose, Matrices, exercise. This expansive textbook survival guide covers 101 chapters, and 4221 solutions. Since the solution to 12E from 2.6 chapter was answered, more than 229 students have viewed the full step-by-step answer. Discrete Mathematics and Its Applications was written by and is associated to the ISBN: 9780073383095. The answer to “In this exercise we show that matrix multiplication is distributive over matrix addition.a) Suppose that A and B arc m × k matrices and that C is a k × n matrix. Show that (A + B)C = AC + BC.________________b) Suppose that C is an m × k matrix and that A and B are k × n matrices. Show that C(A + B) = CA + CB.” is broken down into a number of easy to follow steps, and 69 words. The full step-by-step solution to problem: 12E from chapter: 2.6 was answered by , our top Math solution expert on 06/21/17, 07:45AM.

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