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Consider the following system of linear equations (over the real numbers) :5a 9a3b 5b~1Write down the correspondling augmented matrix and reduce it to row echelon f...

Question

Consider the following system of linear equations (over the real numbers) :5a 9a3b 5b~1Write down the correspondling augmented matrix and reduce it to row echelon form_ How many free variables does the system have? Please justify your aSWCr _ Does the system have unique solution? Please justify yOur al- swer; and solve the system of equations

Consider the following system of linear equations (over the real numbers) : 5a 9a 3b 5b ~1 Write down the correspondling augmented matrix and reduce it to row echelon form_ How many free variables does the system have? Please justify your aSWCr _ Does the system have unique solution? Please justify yOur al- swer; and solve the system of equations



Answers

Consider the following augmented matrix. For what value(s) of $a$ does the corresponding system of linear equations have infinitely many solutions? One solution? Explain your answers.$$\left[\begin{array}{lll|r}1 & 0 & 0 & -2 \\0 & 1 & 0 & 5 \\0 & 0 & a & 0\end{array}\right]$$.

Did his are question or more? 43 now to allow infection. Oh, we need to Monte prior or three by two. Right? Your attorney multiply by two of your postural and second bones are entities. Now they want to makes zero for here. Right? Storeroom. Creationists are three minus one. So here to minus 201 minus 103 minor, 30 and 10 minus one. That is mine. Right? So on the hydro we can write any gration that he's Ciro X. But Syria. Why last heroes And his equal nine. Right. You're zero x zero through always also zero and zero. That is also 0.9 right, hero Placido. Placido. It cannot be equal. Do nine, right. We consider that the system is inconsistent and the system s no solution. Thank you.

Did his are question or more? 43 now to allow infection. Oh, we need to Monte prior or three by two. Right? Your attorney multiply by two of your postural and second bones are entities. Now they want to makes zero for here. Right? Storeroom. Creationists are three minus one. So here to minus 201 minus 103 minor, 30 and 10 minus one. That is mine. Right? So on the hydro we can write any gration that he's Ciro X. But Syria. Why last heroes And his equal nine. Right. You're zero x zero through always also zero and zero. That is also 0.9 right, hero Placido. Placido. It cannot be equal. Do nine, right. We consider that the system is inconsistent and the system s no solution. Thank you.

So reading his linear equations is pretty straight forward. We're gonna have X plus five Z because negative nine from our first round in the Matrix. Then we'll have why minus two Z equals four from our second row and then where I am, zero z equals three from Mark their growth. Now, from this third equation, we can see that zero equals three. So, in fact, this linear system will never be satisfied. Because this is a contradiction on this can never happen, so there is no solution.

Were given with this system off linear equations which can be returned in matrix form as a Matics off coefficients, that is 2314 multiplied with a variable metrics, that is X one and X two equals toe the constant metrics that is five and then which can symbolically be returned as X equals two B. Now, to solve these, we can write it in the form of augmented metrics. We have our augmented metrics, as is to be, which gives us 2314 equals 25 and 10. To solve this by using goes Jordan method. We heard we need that they're diagonal elements is one and the other elements a zero in the side off a and the corresponding changes and be will give us the solutions for expanding next to. So let's start with making the first element is one so we can perform the operation are one transforms to our one minus Artal. Hence we get one three minus full is negative one and five minus 10 is negative. Five. We have one full and then next begin perform. I do transforms to our two minus our one and we get the first rule is thirties and the second row becomes zero. Four plus one is five and 10 plus five is 15 now to make the second rule. Second element is one we can perform are two transforms to one divided by five multiplied with our do. Hence we get one negative one negative five 013 Further to solve. We need the negative Ellen Element to become zero chance we can perform. Our one transforms to R one plus R two, which gives us 1001 Transforms to negative five plus three is negative two. And here we have three. Hence a Vol Excellent equals to a negative, too, and X two equals to treat. That is over. Answer. We can check this by using over metrics calculator. We have this medicine metric system system of equations calculator really input the equations to go. The questions of the hair is coefficient off X minus two and coefficient of extra is three and we have to Constant as five for second equation were proficient affects one is one coefficient of Extras four and the constant extent. So we need to solve these by using Gore's Jorden elimination and we get the solution as explaining question. Negative to an extra close to three hands. This is a very fact. Thank you.


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