# Using matrices solve the following system of equations:x + y – z = 3; 2x + 3y + z = 10; 3x – y – 7z = 1

Given: system of equations: x+y–z=3; 2x+3y+z=10; 3x–y–7z=1

To find: the solution of the given system of equation using matrices

given system of equations is

x+y–z=3

2x+3y+z=10

3x–y–7z=1

Now we will write the system of equation as AX=B,

i.e., in matrix A there will be coefficients of x, y and z,

in matrix X there will be variables x, y and z,

in matrix B will all the constant terms,

so the given system of equations can be written as So Now we will solve for |A|, i.e., determinant of matrix A, so  |A|=1(3× (-7)-1× (-1))-1(2× (-7)-1× 3)-1(2× (-1)- 3× 3)

|A|=1(-21+1)-1(-14-3)-1(-2-9)

|A|=1(-20)-1(-17)-1(-11)

|A|=-20+17+11

|A|=8…………..(i)

As |A|≠0, the given system of equation is consistent and has unique solution

Now given system of equation is written as

AX=B

Now the solution of the given system of equation can be calculated as

X=A-1B  And Now we know

The adjugate, classical adjoint, or adjunct of a square matrix is the transpose of its cofactor matrix.           A11=(-1)1+1.M11=(-1)2.(-20)=-20

A12=(-1)1+2.M12=(-1)3.(-17)=17

A13=(-1)1+3.M13=(-1)4.(-11)=-11

A21=(-1)2+1.M21=(-1)3.(-8)=8

A22=(-1)2+2.M22 =(-1)4.(-4)=-4

A23=(-1)2+3.M23=(-1)5.(-4)=4

A31=(-1)3+1.M31=(-1)4.(4)=4

A32=(-1)3+2.M32=(-1)5.(3)=-3

A33=(-1)3+3.M33=(-1)4.(1)=1

Thus, Now, substituting the above value in equation (iii), we get Substituting value from equation (i) in above equation, we get Substituting this value in equation (ii), we get Multiplying the two matrices, we get     On equating we get

x=3, y=1, z=1

Hence the solution of the given system of equation using matrices is x=3, y=1, z=1

Rate this question :

How useful is this solution?
We strive to provide quality solutions. Please rate us to serve you better.
Related Videos  All About Faraday's law55 mins  Know all about Infertility39 mins  Revision Class | All Formulas of Electrodynamics63 mins  Get to know all about Immune SystemFREE Class  Know All About Types of Relations53 mins  Know all about Colligative Properties50 mins
Try our Mini CourseMaster Important Topics in 7 DaysLearn from IITians, NITians, Doctors & Academic Experts
Dedicated counsellor for each student
24X7 Doubt Resolution
Daily Report Card
Detailed Performance Evaluation view all courses 