Please please please please please.... please help me. In section 5.3 we used Cramer's Rule to find the solution to Ax = b for the specific variable x.To do this, we replaced the j-th column of the coefficient matrix A with the vector b to get thematrix Bj. Then,det(B)X, = det(A)We can use Cramer's Rule to find the inverse of a matrix one entry at a time:Since AA-1 = 1, if we multiply A by the first column of A-1 we should get the first column of I.Likewise, if we multiply A by any other column of A-1 we get the corresponding column of I.|1 3 -1]1. Let A =|-1 2 1. Let bị = 0(i.e. the first column of I) and solve Ax = bị using-2 -2 3Cramer's Rule (to get the first column of A-1). Note that this will require using Cramer'sRule three times, once for each component.2. Now let bz = 1 and solve Ax = b2.3. Solve Ax = bz one last time with bz =4. Use the results of the first three questions to write A-1.In general, we can find the ij-th entry of A- by using Cramer's Rule, replacing the i-th column ofA with the j-th column of 1. Then, the determinant of this matrix can be found using cofactorexpansion down that i-th column. The only nonzero term of that expansion will be in the j-th row.This gives us:det(B1) _ (–1)**/ det(M1)det(A)det(A)where Mji is the "minor" matrix obtained by removing the j-th row and i-th column of A. Noticein particular that, because of our earlier construction, the row and column are flipped! The ij-thentry of A- depends on the cofactor of the ji-th entry of A.We can simplify the notation by creating a "cofactor matrix" C, whose ij-th entry is the cofactorof the ij-th entry of A. Then:CTA-1det(A)5. Find the cofactor matrix for A =and use it to find A-16. Find the cofactor matrix for a 2Iand use it to generate the formula for a 2-by-2 inverse.

Name: Please please please please please.... please help me. In section 5.3
Uploaded: 2024-03-20T07:07:37.000Z
Channel: Bartleby
Description: Please please please please please.... please help me. In section 5.3 we used Cramer's Rule to find the solution to Ax = b for the specific variable x.To do this, we replaced the j-th column of the coefficient matrix A with the vector b to get thema