Solve the systems of equations using matrices.4x+y+z=3-x+y-2z=-11x+2y+2z=-1

Amari Flowers

Amari Flowers

Answered question

2021-03-06

Solve the systems of equations using matrices.
4x+y+z=3
x+y2z=11
x+2y+2z=1

Answer & Explanation

gotovub

gotovub

Skilled2021-03-07Added 98 answers

Step 1
Write all the coefficients of x in one column, all the coefficients of y in one column and all the coefficients of z in one column to obtain the A matrix.
Wite x ,y ,z in one column of a matrix to obtain the matrix of variables be X matrix.
write all the constants in a single column of matrix to get the matrix of all constants let it be B matrix.
Take the dot product of A matrix and X matrix and equate it to B matrix to get it in the form AX=B.
[411112122][xyz]=[3111]
Step 2
Find the inverse of A matrix and multiply it with B matrix to obtain the value of x,y,z.
Find the matrix of minors and apply alternate negative sign on elements of the matrix to obtain the matrix of cofactors.
take the transpose of the matrix of cofactors and multiply it by the determinant of A matrix to obtain the inverse matrix.
[2+42+222228181218+14+1]=[603077375]
=[(+)6()0(+)3()0(+)7()7(+)3()7(+)5]
=[603077375]
AdjA=[603077375]
A1=[603077375](121)
=[27013013131713521]
Step 3 Substitute the value of A1 in X=A1 B to obtain the values of x,y,z.
[xyz]=[27017013131713521][3111]
=[67+0+1701131337113521]
[xyz]=[143]
thus the value of x is 1, y is -4 and z is 3.

Jeffrey Jordon

Jeffrey Jordon

Expert2022-01-27Added 2605 answers

Answer is given below (on video)

Jeffrey Jordon

Jeffrey Jordon

Expert2022-08-23Added 2605 answers

Answer is given below (on video)

Do you have a similar question?

Recalculate according to your conditions!

Ask your question.
Get an expert answer.

Let our experts help you. Answer in as fast as 15 minutes.

Didn't find what you were looking for?