marklynr9955
02.03.2020 •
Mathematics
The 2-by-2 system is simple enough so that you can solve it by any means you know. However, the relations among N(A), C(A), solvable RHS, and all solutions, which should show up in the graphs, are the same for systems of any size or shape. Consider the following system of equations.
3x₁ - 2x₂ = b₁
6x₁ - 4x₂ = b₂
You will sketch two different graphs. You need relatively accurate graphs in order to answer part (f) which is the main point of this whole exercise.
(a) If we write the above system using matrix notations Ax = 5, what is the coefficient matrix A, what is 7, and what is b?
(b) What does it mean to say that the system is homogeneous? What is the definition of the nullspace of a given matrix? Describe the nullspace N(A) of this particular A in any way you can (pictures, equations, words, ...).
(c) What is the definition of the column space of a given matrix? Describe the column space C(A) of this particular A in any way you can.
(d) Choose three different right-hand vectors b ≠ 0 for any of which the system does NOT have a solution. On your first graph, sketch N(A), C(A), and these three b's.
(e) Choose two other different right-hand vectors b ≠ 0 for which the system DOES have a solution. Solve the system for each B's. How many solutions are there for each b? On your second graph, sketch N(A), C(A), these two b's, and all solutions corresponding to each b.
(f) Study your two graphs and notice any special relationship(s) among various objects. Complete the following sentences.
i. In order for At = 5 to have a solution, the right-hand vectors b (Hint: relate to C(A) and/or N(A)).
ii. In the case that Ac = b is solvable, all its solutions form C(A) (Hint: relate to C(A) and/or N(A)).
Solved
Show answers
More tips
- H Health and Medicine Boosting Immunity: A Complete Guide on How to Improve Your Body’s Natural Defenses...
- C Computers and Internet The Best Antivirus Programs for your PC...
- H Health and Medicine Angina: Causes, Symptoms, and Treatment...
- C Computers and Internet How to Learn to Type Fast?...
- F Food and Cooking Delight for Gourmets: How to Prepare Liver Pate...
- S Style and Beauty How to braid friendship bracelets?...
- H Health and Medicine Mercury Thermometer Danger: What to do when a thermometer breaks?...
- F Food and Cooking Which Calamari Salad is the Most Delicious?...
- S Society and Politics 10 Tips for Boosting Your Self-Esteem...
- F Food and Cooking The Most Delicious and Simple Fish in Batter Recipe...
Answers on questions: Mathematics
- M Mathematics e) two years hence a boy will be two times as old as a girl before four years he was three times as old as the girl was. find their presents....
- M Mathematics If you divide an inheritance of $456000 among 22 heirs what will each hero receive...
- M Mathematics shelley sold one customer 5 peanut butter biscuits for $3. she sold another customer 7 beef treats for $4.20.because the cross products are equal, which statements are...
- M Mathematics What is the range of y =|3x + 11?...
- M Mathematics ∠a=6x+5 ∠b=4x+45 solve for x and then find the measure of ∠a...
- M Mathematics Is 0.0004 greater or less than 0.73...
- M Mathematics An isometry preserves all the following except a)distance b)shape c)orientation d)size...
- M Mathematics For figure abcdef shown here, identify the image after each transformation described. for example, a reflection across ad has an image of figure afedcb. in the figure,...
- M Mathematics The sum of three numbers in ap is 36 . when the numbers are increased by 1, 4, 43 respectively. the resulting numbers are in gp. find the numbers....
- M Mathematics What is -6x-2y=-4 using substitution...
Ответ:
Step-by-step explanation: see attachment below
Ответ:
The correct values are 7 and 8 respectively.
Step-by-step explanation:
We need to go through two steps before we can find out both values.
1. Trial-and-error with values
We know that x and y need to be greater than 6 and less than 10.
Therefore: , , and .
Now, insert two random values that fit within the inequalities (x = 7, y = 8).
Our new sequence is .
2. Check median and mean of data set
Now, using our new sequence, find the median.
Median is middle value of the data set, so our median is 7.
Now, find the mean of the data set.
Mean is the average of the sum of the data set, so:
Our mean and median are equal, so we can infer that and .