1answer.
Ask question
Login Signup
Ask question
All categories
  • English
  • Mathematics
  • Social Studies
  • Business
  • History
  • Health
  • Geography
  • Biology
  • Physics
  • Chemistry
  • Computers and Technology
  • Arts
  • World Languages
  • Spanish
  • French
  • German
  • Advanced Placement (AP)
  • SAT
  • Medicine
  • Law
  • Engineering
vodka [1.7K]
3 years ago
9

Suppose the solutions of a homogeneous system of four linear equations in five unknowns are all multiples of one nonzero solutio

n. Will the system necessarily have have a solution for every possible choice of constants on the right sides of the​ equations? Explain.
Mathematics
1 answer:
Akimi4 [234]3 years ago
8 0

Consider a homogeneous machine of four linear equations in five unknowns are all multiples of 1 non-0 solution. Objective is to give an explanation for the gadget have an answer for each viable preference of constants on the proper facets of the equations.

Yes, it's miles true.

Consider the machine as Ax = 0. in which A is 4x5 matrix.

From given dim Nul A=1. Since, the rank theorem states that

The dimensions of the column space and the row space of a mxn matrix A are equal. This not unusual size, the rank of matrix A, additionally equals the number of pivot positions in A and satisfies the equation

rank A+ dim NulA = n

dim NulA =n- rank A

Rank A = 5 - dim Nul A

Rank A = 4

Thus, the measurement of dim Col A = rank A = five

And since Col A is a subspace of R^4, Col A = R^4.

So, every vector b in R^4 also in Col A, and Ax = b, has an answer for all b. Hence, the structures have an answer for every viable preference of constants on the right aspects of the equations.

You might be interested in
ny with 350 employees is changing the employee health insurance plan to either plan A or plan B. The company wants to know if em
Marianna [84]

Answer:

All the conditions for the chi square test of homogeneity are satisfied.

Step-by-step explanation:

The conditions for the chi square test  are

1) the sample is a random sample

2) the variable under study is categorical

3) all expected value of the number of sample observations are greater or equal to 5.

A)The observations must be independent

B) for 2 categories the expected values must be at least 5

C) for the 3 categories the expected values must be at least 1 and no more than 20% may be smaller than 5

The observations given are independent that is not equally likely i.e do not have equal chances of occurrences or are not dependent on each other.

4) the overall sample must be resonably large that is greater than 50

7 0
3 years ago
A pair of dice was rolled 50 times and the results are in the accompanying table. From these results, calculate an
Snezhnost [94]

Answer:

Step-by-step explanation:

5 0
3 years ago
X=3m/2-m <br><br>make m the subject of the formula<br>help me plss
wel

Answer:

2X/(3+X)

Step-by-step explanation:

X = 3m/2-m

Cross multiply both sides

X × (2-m)= 3m

2X-Xm= 3m

2X= 3m+Xm

2X= m(3+X)

Divide both sides by the coefficient of m which is (3+X)

m= 2X/(3+X)

8 0
2 years ago
Every integer is an irrational number.<br><br> True<br><br> False
Westkost [7]

Answer: true

Step-by-step explanation:

6 0
3 years ago
Read 2 more answers
Factor this equation , I can’t comprehend it
ivolga24 [154]

Answer:

B) (2x + 3)(2x - 3)

Step-by-step explanation:

Use the FOIL method for each answer choice.

FOIL = First, Outside, Inside, Last

(2x)(2x) = 4x²

(2x)(-3) = -6x

(3)(2x) = 6x

(3)(-3) = -9

4x² -6x +6x  -9

Simplify. Combine like terms:

4x² (-6x + 6x) - 9

4x² - 9

4x² - 9 = 4x² - 9 ∴ B) (2x + 3)(2x - 3) is your answer

~

8 0
3 years ago
Read 2 more answers
Other questions:
  • You are planning to email to two lists. the first list has 1,200 names. the second list has 900 names. there are 150 names that
    6·2 answers
  • Which property of exponents must be used first to solve this expression? (xy^2)^1/3
    11·1 answer
  • A boy ate 100 cookies in5 days. Each day he ate6 more than the day before. How many cookies did he eat the first day?
    11·1 answer
  • 17.83 rounded to the nearest tenth
    14·1 answer
  • Suppose you need to deliver 40 terabytes of data to your co-workers in Atlanta (200 km). You have an available 100 Mbps dedicate
    8·1 answer
  • I am a 2 dimensional shape that had 5 obtuse angles
    12·1 answer
  • NEED HELP ASAP!! ANSWER A THROUGH F PLEASE!!
    9·1 answer
  • Using the measurements given below, find the hypotenuse of the triangle.
    10·1 answer
  • Please any help? anybody ​
    6·1 answer
  • Lucy is a waitress. At the end of the night she must give 12% of her tips to the cleaning crew. How much does she go home with i
    13·2 answers
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!