Please will upvote! Determine whether the non-homogeneous system of linear equations givenbelow is consistent. If so, write the solution in the form x = xp + Xh where x, is aparticular solution of Ax=b and xr is a solution of Ax=0 (the homogeneoussolution).2x + 6y + 20z = 18-2x + 7y + 32z = 29-x + 3y + 14z = 123x + 3y + 6z = 24%3D

Name: Please will upvote! Determine whether the non-homogeneous system of li
Uploaded: 2024-03-20T07:07:37.000Z
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Description: Please will upvote! Determine whether the non-homogeneous system of linear equations givenbelow is consistent. If so, write the solution in the form x = xp + Xh where x, is aparticular solution of Ax=b and xr is a solution of Ax=0 (the homogeneoussol

The system of equations are, 2x+6y+20z=18-2x+7y+32z=29-x+3y+14z=123x+3y+6z=24 The system of equations can be written in the matrix form Ax=b as follows. 2620-2732-1314336xyz=18291224 The augmented matrix AB is, 262018 -273229 -131412 33624The system of equation is consistent only if the rank of A is equal to rank of AB. Find the rank of the matrices using the Gaussian elimination method as follows. 262018 -273229 -131412 33624 First make the elements below 2 in first column as zeros. 262018 0135247 -131412 33624 R2+R1→R2262018 0135247 062421 33624 R3+12R1→R3262018 0135247 062421 0-6-24-3 R4-32R1→R4Now, make the elements below 13 in second column as zeros. 262018 0135247 000-913 0-6-24-3 R3-613R2→R3262018 0135247 000-913 00024313 R4+613R2→R4262018 0135247 000-913 0000 R4+27R3→R4That is, 262018 -273229 -131412 33624≡262018 0135247 000-913 0000 That is, there are two nonzero rows for the matrix A. Therefore, Rank(A)=2 But the rank of the augmented matrix is,RankAB=3. That is, Rank(A)≠Rank(AB). Therefore, the system is not consistent and so it has no solution.