Okay. The idea behind this problem is to use the idea of an inverse matrix to solve a system of linear equations. The process involves this principle that Matrix X equals the inverse of matrix A times matrix speak now, Matrix X stands for the variable matrix matrix A. Is the coefficient matrix from your system and Matrix B is the constant matrix from your system. So basically this principle is saying mr verbal matrix will equal the inverse of the coefficient matrix times the constant matrix. So too big tasks in this problem are to find the inverse of the coefficient matrix and then to multiply that in verse times of constant magics. So the problem that we are working with, Yeah, yes. I. System that has three equations, three variables. So the terrible matrix is going to be X, Y and Z. Oh, the coefficient matrix in this problem is 25 61 -12. And that's the X, YZ coefficients from the first equation. Yeah. And then 18 negative 12 positive seven. Again, coefficients of x Y Z from the second equation. And then three, four negative woman Coefficients of X, YZ from the 30 question. So the inverse of that is going to be multiplied times the constant matrix, Which is a 10 negative nine, 12. So again, the big task on this is to get the inverse of the coefficient matrix. And then the next big task is multiply that inverse times the constant matrix. But in a previous problem you were to find the inverse matrix. Yeah, Around it to two decimal places. So that inverse matrix was and took to two decimal places zero T. Is there a zero T 0.40 More? And then 0.06. 0.0 T -0.57. And then 0.16 Yeah. 0.12. And there were 2.7. Look, okay, that was the first major expanding the previous problem for this uh, coefficient matrix. Well multiply that times the constant metrics. Okay, Okay. Someone moving space. I can do some computations. Yes. So we will take the first row times are constantly took. So that's going to be a negative 0.02. The 0.02 and 0.40 more. We do the multiplication will have a negative point to A- -18. and at four 92 And that evaluates it works out or sympathize to four 54. Mhm. Okay. Race this. We can do the second row. I want to Okay then. With the second row of the universe metrics times the constant matrix. Again. These numbers down so can keep track of what needs to be multi broad. Okay, that works out. 2.6 negative 0.18 In a negative 6.84 combine those and we get a negative 6.42. Okay, race those and do the last one. Okay. Yeah. Question mm. Money. Okay. The last round Of the Inverse Matrix, that's going to be a single .16. The remote papa 0.12 and a negative 2.5 kids modification is gonna get us at 1.6 negative 1. 8 And a negative 24.6 Combine those and we will end up with a negative 24.08. So we have solved the system to two decimal places. We have our X why and I see so we can ride in order triple. Again these are rounded to two decimal places. We've got our X. Why and R C. Yeah. Okay. And that solves that system using inverse matrix.