Given a linear system of equations below. The matrix equation of the linear system is given

tricotasu 2021-01-10 Answered

Given a linear system of equations below. The matrix equation of the linear system is given by: (see image)
Given a linear system of equations below.The matrix equation of the linear system is given by:Ax=b.The determinant of A is 8.Using Cramers's rule find the value for x.
x+3y+4z=3
2z+6y+9z=5
3x+y2z=7

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Expert Answer

casincal
Answered 2021-01-11 Author has 82 answers

Consider the provided system of equation
x+3y+4z=3
2z+6y+9z=5
3x+y2z=7
The matrix equation of the linear system is given by,
AX=b
Where, A[(1,3,4),(2,6,9),(3,1,2)]
given, |A|=8
Find the value of x by using cramer's rule
x=|Dx||D|
here, Dx=[(3,3,4),(5,6,9),(7,1,2)]
and, |D| is the determinant of the matrix A
Since,when system of equation as,
a1x+b1y+c1z=d1
a2x+b2y+c2z=d2
a3+b3+c3z=d3
Then, Dx=[(d1,b1,c1),(d2,b2,c2),(d3,b3,c3)]
Now, the value of x find as,
x=|Dx||D|
=|(3,3,4),(5,6,9),7,1,2|A|
=(36+20+189)(168+2730)8
=1731658
=88
=1
Thus, x=1

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