## Question

###### 7. Consider the Theorem: Suppose A and B are two lower triangular matrices (Defined in 8...

7. Consider the Theorem: Suppose A and B are two lower triangular matrices (Defined in 8 3.1), of order n. Then, the product AB is also a lower triangular matrix. Likewise for upper triangular matrices. (We say that the set of lower triangular matrices, of order n, is closed under multiplication.) Prove this theorem, for n = 3, by multiplying the following two matri- ces: a1 0 0 A bi b 0 1 0 0 and B 2 0 21 22 23 Answer: AB-

## Answers

A = (a_1 b_1 c_1 0 b_2 c_2 0 0 c_3) and B = [x_1 y_1 z_1 0 y_2 z_2 0 0 z_3] Both are Lower triangular matrix, Now order to find A B we have AB = [a_1 b_1 0 b_2 c_2 0 0 c_3] [x_1 y_1 z_1 0 y_2 z_2 0 0 z_3] [a_1 x_1 + 0 + 0 b_1 x_1 + b_2 y_1 + 0 c_1 x_1 + c_2 y_1 + c_3 z_1 0 + 0 + 0 0 + b_2 y_2 + 0 0 + c_2 y_2 + c_3 z_2 0 + 0 + 0 0 + 0 + 0 0 + 0 + c_3 z_3] (a_1 x_1 b_1 x_1 + b_2 y_1 c_1 x_1 + c_2 y_2 + c_3 z_1 0 b_2 y_2 c_2 y_2 + c_3 z_3 0 0 c_3 - z_3)_3 times 3 which is the Lower triangular matrix

#### Similar Solved Questions

1 answers

##### 2. Consider the following simultaneous move game: Column Left Right Top 1,1 7,3 Row Bottom 3,5...

2. Consider the following simultaneous move game: Column Left Right Top 1,1 7,3 Row Bottom 3,5 11,0 (a) Find all pure-strategy Nash equilibria (b) Now assume that the game is made sequential with Row moving first. Illustrate this new game using a game tree and find the rollback equilibrium (c) List ...

1 answers

##### If a template DNA strand has the base sequence 3'-GTC...CCA-5, what would be the sequence of...

If a template DNA strand has the base sequence 3'-GTC...CCA-5, what would be the sequence of the corresponding mRNA? (Note: "..." represents an intervening sequence) a. 3 CAG...GGU S' b. 5'CAG.GGU-3 OCCAGGGT-3 O d. 5'-GUC...CCA-5 Oe.3GUC...CCAS'...

1 answers

##### Additional Problem 10 The following errors were discovered on the books of Ivanhoe Inc., during the...

Additional Problem 10 The following errors were discovered on the books of Ivanhoe Inc., during the preparation of the 2020 financial statements, prior to the books being closed for the year. (a) $13,700 of goods held on consignment from Stevens Co were counted as part of Ivanhoe’s invento...

1 answers

##### How much work is done moving a charge along an equipotential surface (line)? Explain.

How much work is done moving a charge along an equipotential surface (line)? Explain....

1 answers

##### [The following information applies to the questions displayed below.] In 2021, the Westgate Construction Company entered...

[The following information applies to the questions displayed below.] In 2021, the Westgate Construction Company entered into a contract to construct a road for Santa Clara County for $10,000,000. The road was completed in 2023. Information related to the contract is as follows: 2021 2022 2023 Cost ...

1 answers

##### S.HCR and Na At what point in the following titration carve for a weak acid being...

S.HCR and Na At what point in the following titration carve for a weak acid being litrated with a strong base is the pH equal to the p. of the acid? The X-atis scale goes from 0.0 ml. to 20.0 ml. The sharp rise is at 100 ml 10 Id 10.0 ml 180 ml...

1 answers

##### Concave mirror: f = 50 mm, d. = 75 mm. Mirror d = 150mm or i5cm...

Concave mirror: f = 50 mm, d. = 75 mm. Mirror d = 150mm or i5cm ho = 20mm or 2cm ha 0.00T - 150mm EMU Department of Physics and Astronomy 2019 Page 139...

1 answers

##### Please help with all the questions. CHM-111 General Chemistry I Problem Set- Chang, Chapter 4A Spring...

Please help with all the questions. CHM-111 General Chemistry I Problem Set- Chang, Chapter 4A Spring 2018 Name: Date: 1. Which of the following species are present in an aqueous solution of NaHCOs, a weak electrolyte? A) Na*, H', co, B) Na+, HCO3 C) NaH, C, 0,2 D) NaHCO3, Na", HCO3 Wr...

1 answers

##### △ABC is a right triangle with right angle C. Side AC is 6 units longer than...

△ABC is a right triangle with right angle C. Side AC is 6 units longer than side BC . If the hypotenuse has length 52–√ units, find the length of AC. courseware-Google Chrome a https://www.casa.uh.edu /Root/Pages/CW aspx?id 643857CE-8CB9-4B21-AC4B-1AD73C216A8D CourseWare Qu...

1 answers

##### Muscle force Axis w The mass and length of the forearm in the diagram below are...

Muscle force Axis w The mass and length of the forearm in the diagram below are 2.2 lbs. and 0.1 m, respectively. Calculate the torque generated by the weight of the forearm, assuming the weight of the forearm is located halfway along the forearm (1 kg = 2.2 lbs.)....

1 answers

##### Write the following as wfs of a theory with equality a) there are at least three...

Write the following as wfs of a theory with equality a) there are at least three moons of Jupiter b) at most two people know everyone in the class...

1 answers

##### On July 1, 2021, Charlie Co. paid $18,000 to Rent-An-Office for rent covering 18 months from...

On July 1, 2021, Charlie Co. paid $18,000 to Rent-An-Office for rent covering 18 months from July 2021 through December 2022. What adjusting entry should Charlie Co. record on December 31, 20217 Multiple Choice O Debit Rent Expense and credit Cash for $18,000 O Debit Rent Expense and credit Prepaid ...

1 answers

##### Your coin collection contains 40 1955 silver dollars. If your grandparents purchased them for their face...

Your coin collection contains 40 1955 silver dollars. If your grandparents purchased them for their face value when they were new, how much will your collection be worth when you retire in 2059, assuming they appreciate at a 11 percent annual rate?...

1 answers

##### Forces in a Three-Charge System l Review Part A What is the net force exerted by...

Forces in a Three-Charge System l Review Part A What is the net force exerted by these two charges on a third charge s-450 nC placed between g and g at -1230 m? Your answer may be postive or negative, depending on the direction of the force. Express your answer numerically in newions to three signif...

1 answers

##### Part 1: Calculate the dimension Given the following matrix: 1 1 A 4 3 -2 4...

Part 1: Calculate the dimension Given the following matrix: 1 1 A 4 3 -2 4 5 -2 16 9-9 -4 4 3 4 -1 Let S be the space spanned by A, that is S span(A) The dimension of Sis: dim S = 1 Part 2: Find a basis Enter a basis B of S below. 0 | -3 7 B=BA 0 0 -1 1 0 0 0 0...

1 answers

##### Use the following roadmap to answer the next three problems. Br PBr3 РСС В А HBr...

Use the following roadmap to answer the next three problems. Br PBr3 РСС В А HBr С Draw the structure of compound A....

1 answers

##### Sites 14 of You are arn by pregnant women during the course of their pregnancies.Your sample...

Sites 14 of You are arn by pregnant women during the course of their pregnancies.Your sample is the next 200 single births occurring in a given hospital. For each birth, a medication history will be taken from the new mother and from her doctor; in addition, you will review medical records to venity...

1 answers

##### Francisco Inc. acquired 100 percent of the voting shares of Beltran Company on January 1, 2017....

Francisco Inc. acquired 100 percent of the voting shares of Beltran Company on January 1, 2017. In exchange, Francisco paid $889,250 in cash and issued 105,000 shares of its own $1 par value common stock. On this date, Francisco’s stock had a fair value of $12 per share. The combination is a s...

1 answers

##### 3.3. The chlorofluorocarbon CFC-12 (CF2Cl2) is removed from the atmosphere solely by photolysis. Its atmospheric li...

3.3. The chlorofluorocarbon CFC-12 (CF2Cl2) is removed from the atmosphere solely by photolysis. Its atmospheric lifetime is 100 years. In the early 1980s, before the Montreal protocol began controlling production of CFCs because of their effects on the ozone layer, the mean atmospheric concentratio...