In Exercises 55–56, write the system of linear equations for whic...

Question

In Exercises 55–56, write the system of linear equations for which Cramer's Rule yields the given determinants. 2 - 4 8 - 4 D = D_x = 3 5 - 10 5

Determinants D and Dx for a system of linear equations in Cramer's Rule.

Accepted Answer

Welcome back. I am so glad you're here. We are given these two determinants and we are to figure out a corresponding system of linear equations using Cramer's rule. So we need to recall previous lessons on Cramer's rule and determinants. And from that we know that a given determinant has corresponding coefficients and these are the positions of those coefficients. So for the determinant, the upper left hand position is a sub one and then going down the column, we have a sub two. And then for the second column we start with B sub one and B sub two for this, D sub X. The determinate in the numerator of X. The corresponding coefficients are for the positions of C sub one and C sub two for the first column. And the second column is again B sub one and B sub two. And here's what they correspond to. We have a system of equations that has a sub one as the coefficient of X plus B. Sub one as the coefficient of why equals the constant term C sub one. That's the first equation in our system of equations. The second one is a sub two, is the coefficient of X plus B. Sub two is the coefficient of Y equals C sub two as the constant term. So now it's just a matter of matching things up. So we want to fill this in, we want to look for a sub one. So we go to the corresponding position in our determinant and that's going to be this upper left hand position in the regular determinant. So the coefficient of X in the first equation is four. So we have four X plus. And now we want to look for B sub one. B sub one is right here in the determinant. So be someone is five. We got five. Y equals the constant term. Well, that is given to us in R D sub X determinant, which is the upper left hand position here. So the coefficient Or the constant term on the right hand side of the equal side is -2. There's our first equation, the second one. Now we're looking for a sub two is the coefficient of X. That's right here, which is seven. So we've got seven X. And now we're looking for B sub two, which is this last spot in the regular determinant? That's negative three. So it's minus three Y. For the coefficient of Y. Now our constant term, we're looking for C. Sub two. That's right here in R D sub X and which is right here, so that equals 11 and that's it. That's our system of equations. We look at our answer choices and this matches with answer choice. C. Well done, we'll catch you on the next one

In Exercises 55–56, write the system of linear equations for which Cramer's Rule yields the given determinants. 2 - 4 8 - 4 D = D_x = 3 5 - 10 5

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