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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.

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8x+5y=35 solve for y no work needed but you can show me the work if you want i will still look at it thank you in advance
solong [7]

Answer:

y=7-(8/5)x

Step-by-step explanation:

To solve for y we need to get Y on one side of the equation all by itself.  To start we can move the 8x to the side with the 35 by subtracting 8x on both sides which gets us to 5y=35-8x then we just need to get the 5 detached from the y and we will have solved for Y.  To do this we can divide by 5 on both sides to cancel out the 5 with the Y which leaves us with y=7-(8/5)x

I hope this helps and please don't hesitate to ask if there is anything still unclear!

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Solve for c 8/3c -2= 2/3c-12
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4. The population of Bay Village is 35,000 today. Every year the
frosja888 [35]

Answer:

Linear Model:   y(x)=35,000+750x

Step-by-step explanation:

In principle <em>Linear Models </em>are employed when we want to define a relationship between an independent and a dependent variable. <em>Linear Models</em> are also known as<em> Functions </em>, where one variable is expressed as a function of <em>at least one</em> other variable. The most common example would be a dependent variable y that is directly linked as a response to any changes of an independent variable x. The most common expression of such relationship would be y=ax where a is the relationship factor between y and x and is also known as the <em>slope </em>of the function (representing a rate of change of that function).

In this question we are told that the population of Bay Village today is 35,000. So we know this is our constant variable, lets call it  b.

Next we know that every year the population is increased by 750 people. So we know that our variable and thus our independent variable is every year which we shall call x and our fixed factor is the 750 increment which we will call a.  

From that we can conclude that:

<em>Year 1 Population: 35,000</em>

<em>Year 2 Population: 35,000 + 750 = 35,750</em>

<em>Year 3 Population: 35,750 + 750 = 36,500 </em>

And so on and so forth.<em> </em>

So we want to express the above as a Linear Model of the form:

<em> y = ax + b   </em>Eqn(1).

Thus from Eqn (1) and all information given (i.e. pluging in values) we finally obtain:

y(x)=35,000+750x

Which for every different value of  x (i.e. every year) we can obtain the new and increased population  y(x).

7 0
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