Show that (a) AB + AC = A(B + C); and (b) BA + CA = (B
Question:
(a) AB + AC = A(B + C); and
(b) BA + CA = (B + C)A.
[In general, if A is an m à n matrix and B, C are n à p matrices, then AB + AC = A(B + C). For n à p matrices B, C and a p à q matrix A, it follows that BA + CA = (B + C)A. These two results are called the Distributive Laws for Matrix Multiplication over Matrix Addition.]
Let
Transcribed Image Text:
L 3 5 , and C=[ 0 3-2 -2 7 6
Fantastic news! We've Found the answer you've been seeking!
Step by Step Answer:
Answer rating: 57% (7 reviews)
a b AB AC ...View the full answer
Answered By
Sheikh Muhammad Ibrahim
During the course of my study, I have worked as a private tutor. I have taught Maths and Physics to O'Level and A'Level students, as well as I have also taught basic engineering courses to my juniors in the university. Engineering intrigues me alot because it a world full of ideas. I have passionately taught students and this made me learn alot. Teaching algebra and basic calculus, from the very basics of it made me very patient. Therefore, I know many tricks to make your work easier for you. I believe that every student has a potential to work himself. I am just here to polish your skills. I am a bright student in my university. My juniors are always happy from me because I help in their assignments and they are never late.
4.90+
14+ Reviews
24+ Question Solved
Related Book For
Discrete and Combinatorial Mathematics An Applied Introduction
ISBN: 978-0201726343
5th edition
Authors: Ralph P. Grimaldi
Question Posted:
Students also viewed these Linear Algebra questions
-
Show that A(B + C) = AB + AC for the example matrices in the previous problem.
-
(a) Show that x3 - (a2 + b2 + c2)x - 2 abc has real roots by considering A. (b) Show that a2 + b2 + c2 ¥ ab + ac + be by considering B. Let c a b b c 0 b c a
-
(a) Show that if A is invertible and AB = AC, then B = C. (b) Explain why part (a) and Example 3 do not contradict one another.
-
Explain how each of the following illustrates one of the four principles of interaction. a. At a college tutoring co-op, students can arrange to provide tutoring in subjects they are good in (like...
-
Discuss the major success factors for the Kuali Financials development effort. The Kuali Financial System is an open-source enterprise financial information system for colleges and universities...
-
Andrew Vazsonyi is the manager of the Spendwise supermarket chain. He would like to be able to forecast paperback book sales (books per week) based on the amount of shelf display space (feet)...
-
The ogive at the right represents the cumulative frequency distribution for SAT scores of college-bound students in a recent year. What score represents the 80th percentile? Percentile 100 90 80 70...
-
Landen Corporation uses a job-order costing system. At the beginning of the year, the company made the following estimates: Direct labor-hours required to support estimated production . . . . . . . ....
-
Discuss the implementation of quality management systems (QMS), such as ISO 9001, in organizations, highlighting the importance of process standardization, continual improvement, and internal audits...
-
The following section is taken from Barton Corp.'s balance sheet at December 31, 2013. Current liabilities Interest payable .................$ 56,000 Long-term liabilities Bonds payable, 7%, due...
-
Perform the following matrix multiplications. (a) (b) (c) (d) (e) (f) 3 70 456 123 3 1 10 1 22 6 3 6 462 317 135 3 003 0 100 beh 9 001 100
-
Find the multiplicative inverse of each of the following matrices if the multiplicative inverse exists. (a) (b) (c) (d) 2 3 0 0 1 2
-
Why do companies need policy deployment? What does it do?
-
Mercer Corp. is a firm with 10 million shares outstanding and $84 million worth of debt outstanding. Its current share price is $73. Mercers equity cost of capital is 8.5%. Mercer has just announced...
-
Zetatron is an all-equity firm with 270 million shares outstanding, which are currently trading for $23.64 per share. A month ago, Zetatron announced it will change its capital structure by borrowing...
-
Describe the major elements and issues with an object-oriented approach to developing information systems.
-
Cisoft is a highly profitable technology firm that currently has $5 billion in cash. The firm has decided to use this cash to repurchase shares from investors, and it has already announced these...
-
Suppose Microsoft has 7.26 billion shares outstanding and pays a marginal corporate tax rate of 31%. If Microsoft announces that it will pay out $42 billion in cash to investors through a combination...
-
What types of information do the four organizational levels common to many businesses need?
-
For liquid water the isothermal compressibility is given by; where r and b are functions of temperature only. If 1 kg of water is compressed isothermally and reversibly from I to 500 bar at 60(C. how...
-
Determine the basin of attraction for each constant solution of the autonomous equations in Problems. That is, sketch a direction field and highlight the equilibrium solutions. For each, color the...
-
For the DEs in Problems, use appropriate software to draw direction fields. Then discuss what you can deduce about their solutions by sketching some representative solutions folk>wing the direction...
-
Verify that y = cet is a solution for any real c. of y' = 2ty determine c so that y(0) = 2
-
You are working in a clinic and have just roomed a patient. When you come out of the room, you overhear me complaining to two co-workers about you and how slow you are. [Take the role of the other...
-
What are the advantages and pitfalls of the media's appetite for telling and selling stories? As we reach the point where almost all media exist on the Internet in some form, how have our culture and...
-
When looking at a project to convert data into information, data analysis is the methodology thatshould be used to accomplish the output. When reviewing the tools used in the course and the data that...
Study smarter with the SolutionInn App