10. Prove the following properties of matrix multiplication, where A and B are m x k matrices, C and D are k × n matrices, and r is a scalar: (А + B)С %3D АС + ВС. Hint: partition A and B into rows, and use the row version of matrix multiplication from Exercise 13, Section 3.3. Since each row of A or B is from R, as part of your proof, you will need to show that: а. if 7 and s are from R², then (7 +3)C = 7C + $C.
10. Prove the following properties of matrix multiplication, where A and B are m x k matrices, C and D are k × n matrices, and r is a scalar: (А + B)С %3D АС + ВС. Hint: partition A and B into rows, and use the row version of matrix multiplication from Exercise 13, Section 3.3. Since each row of A or B is from R, as part of your proof, you will need to show that: а. if 7 and s are from R², then (7 +3)C = 7C + $C.
Linear Algebra: A Modern Introduction
4th Edition
ISBN:9781285463247
Author:David Poole
Publisher:David Poole
Chapter2: Systems Of Linear Equations
Section2.3: Spanning Sets And Linear Independence
Problem 42EQ
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3.4 #10
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Transcribed Image Text:10. Prove the following properties of matrix multiplication, where A and B are m x k
matrices, C and D are k × n matrices, and r is a scalar:
(A + B)C = AC + BC.
Hint: partition A and B into rows, and use the row version of matrix multiplication
from Exercise 13, Section 3.3. Since each row of A or B is from R“, as part of your
proof, you will need to show that:
а.
if 7 and 3 are from R*, then (7 +3)C = 7C + 3C.
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