
Concept explainers
(a)
To show: The scalar distributive property of matrices is true for all
(a)

Answer to Problem 47HP
The proof is given below.
Explanation of Solution
Use variable to represent the matrices and scalar in order to show scalar distributive property.
In order to show the scalar distributive property of matrices is true for all
Further simplified as:
Further simplified as:
The proof is given above.
(b)
To show: The matrix distributive property of matrices is true for all
(b)

Answer to Problem 47HP
The proof is given below.
Explanation of Solution
Use variable to represent the matrices and scalar in order to show matrix distributive property.
In order to show the matrix distributive property of matrices is true for all
Further simplified as:
Further simplified as:
The proof is given above.
(c)
To find: The associative property of multiplication of matrices is true for all
(c)

Answer to Problem 47HP
The proof is given below.
Explanation of Solution
Use variable to represent the matrices and scalar in order to show matrix distributive property.
In order to show the associative property of multiplication matrices is true for all
Further simplified as:
Further simplified as:
The proof is given above.
d)
To show: The associative property of scalar multiplication of matrices is true for all
d)

Answer to Problem 47HP
The proof is given below.
Explanation of Solution
Use variable to represent the matrices and scalar in order to show scalar distributive property.
In order to show the scalar distributive property of matrices is true for all
Further simplified as:
Further simplified as:
The proof is given above.
Chapter 4 Solutions
Algebra 2
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